Polynomial Smoothing Research Articles

Estimating Sharpe ratio function in the presence of measurement error

In financial econometrics, the Sharpe ratio function serves as a gold standard to measure the return-to-risk ratio for comparing different assets or trading strategies. In the recent literature, several methods have been developed to directly or indirectly estimate the Sharpe ratio function, yet none of them apply to the scenario where the covariates are measured with error. To handle this problem, we propose a new method by incorporating the local polynomial smoothing and SIMEX to simultaneously estimate the Sharpe ratio function and the negative log-volatility function in the presence of measurement error. The asymptotic bias and variance of the proposed estimators are also derived under some regularity conditions. We further conduct Monte Carlo simulations to evaluate the finite sample performance, and apply two real data examples to illustrate the usefulness of our new method.

Development of Criteria for Assessing Nutritional Status in Moscow Adults Using Bioimpedance Analysis Data

Objective. To develop the criteria for assessing nutritional status in Moscow adults using bioimpedance analysis data.Materials and methods. The research used data from a non-clinical, cross-sectional, observational study on the body composition of Moscow adults aged 18-96 in Moscow health centers between 2010 and 2019 by the method of bioimpedance analysis. A total of 340,814 persons were assessed, including 96,780 men and 244,034 women. Bioimpedance measurements were taken using bioimpedance analyzers according to a standard four-electrode assessment scheme in the supine position of patients with disposable bioadhesive ECG-electrodes. The relative fat mass (RFM) was assessed using the percentage of fat mass (%FM) and the fat mass index (FMI). The criteria for assessing RFM were the cut-offs of %FM and FMI calculated based on the centiles of BMI thresholds according to the IOTF ageand sex-specific criteria. Polynomial smoothing was then applied. In the same way, the criteria for assessing the relative fat-free mass (RFFM) were derived based on the cut-offs of the fat-free mass index (FFMI).Results. Diagnostic tables were designed to determine the RFM and RFFM in Moscow adults. The prevalence of normal weight obesity was assessed.Conclusion. In conjunction with the previously developed criteria for assessing the nutritional status of Moscow children and adolescents, the study results can be used in clinical, preventive, or sports medicine to diagnose and correct nutritional status disorders as well as to monitor physical development.

Development of Criteria for Assessing Nutritional Status in Moscow Children and Adolescents Using Bioimpedance Analysis Data

Background. Body composition assessment plays an important role in characterizing physical development, monitoring health status, diagnosing nutritional disorders, and assessing disease risks.Objective. To develop the criteria for assessing nutritional status in Moscow children and adolescents using bioimpedance analysis data.Materials and methods. The research used data from a non-clinical, cross-sectional, observational study on the body composition of children and adolescents aged 5–17 in Moscow health centers from 2010 to 2019 by the method of bioimpedance analysis. A total of 115,200 persons were assessed, including 61,430 boys and 53,770 girls. Bioimpedance measurements were taken using bioimpedance analyzers according to a standard four-electrode assessment scheme in the supine position with disposable bioadhesive ECG-electrodes placed on the patient’s wrists and ankles. The relative fat mass (RFM) was assessed using the percentage of fat mass (%FM) and the fat mass index (FMI). The criteria for assessing RFM were the cut-offs of %FM and FMI calculated based on the centiles of BMI thresholds according to the IOTF ageand sex-specific criteria. Polynomial smoothing was then applied. In the same way, the criteria for assessing the relative fat-free mass (RFFM) were derived based on the cut-offs of the fat-free mass index (FFMI).Findings. Diagnostic tables were designed to determine the RFM and RFFM in Moscow children and adolescents. The prevalence of normal weight obesity was assessed.Conclusion. The study results can be used in clinical, preventive, or sports medicine to diagnose and correct nutritional status disorders as well as to monitor physical development.

Isotonic Regression for Variance Estimation and Its Role in Mean Estimation and Model Validation

We study isotonic regression which is a nonparametric rank-preserving regression technique. Under the assumption that the variance function of a response is monotone in its mean functional, we investigate a novel application of isotonic regression as an estimator of this variance function. Our proposal of variance estimation with isotonic regression is used in multiple classical regression problems focused on mean estimation and model validation. In a series of numerical examples, we (1) explore the power variance parameter of the variance function within Tweedie’s family of distributions, (2) derive a semi-parametric bootstrap under heteroscedasticity, (3) provide a test for auto calibration, (4) explore a quasi-likelihood approach to benefit from best-asymptotic estimation, and (5) deal with several difficulties under Lognormal assumptions. In all of these problems we verify that the variance estimation with isotonic regression is essential for proper mean estimation and beneficial compared to traditional statistical techniques based on local polynomial smoothers.

Thermodynamic and transport properties of binary mixtures containing 1,2-propanediol with 2-methoxyethanol and 2-ethoxyethanol at different temperatures

In the present investigation density, speed of sound, and viscosity have been reported for binary liquid mixtures of 1,2-propanediol (1,2-PD) with 2-methoxyethanol (2-ME) and 2-ethoxyethanol (2-EE) over the entire composition range at T= (298.15–323.15) K. From the experimental data, excess molar volume, (VmE), excess isentropic compressibility, (κsE), excess molar isentropic compressibility, (κs,mE), excess speed of sound, (uE), excess isobaric thermal expansion,αpE, and deviation in viscosity (Δη) of liquid mixtures have been calculated. The excess partial molar volume,V¯m,1E, V¯m,2E , excess partial molar isentropic compressibility, K¯s,m,1EK¯s,m,2E over the whole composition range together with partial molar volume,V¯m,10, V¯m,20, partial molar isentropic compressibility K¯s,m,10,K¯s,m,20, excess partial molar volume,V¯m,10E, V¯m,20E and excess partial molar isentropic compressibility, K¯s,m,10E,K¯s,m,20E at infinite dilution have also been calculated. All excess properties have been correlated using the Redlich-Kister smoothing polynomial equation. The VmE results are analysed in the light of Prigogine-Flory-Patterson theory. Analysis of each of the three contributions viz. interactional, free volume, and P* to VmE has shown that interactional contribution and free volume effect are negative for all the mixtures, and P* contribution is positive for the mixtures of 2-ME. The variations of these parameters with changes in composition and temperature have been discussed in terms of intermolecular interactions prevailing in these mixtures. Further, the viscosities of these binary mixtures were correlated theoretically by using various empirical and semi-empirical models and the results were compared with the experimental findings.

Qualitative and quantitative detection of microplastics in soil based on LIF technology combined with OOA-ELM/SPA-PLS

Traditional methods for detecting soil microplastics include chemical digestion, density separation, staining, etc. These methods often only provide qualitative analysis of microplastics and are difficult to accurately quantify. To address this issue, laser induced fluorescence (LIF) technology is introduced, which can achieve high sensitivity, non-destructive, and rapid detection, and improve the accuracy and efficiency of qualitative and quantitative analysis of soil microplastics. Therefore, based on LIF technology, a qualitative prediction model for optimizing Extreme Learning Machine (ELM) using Osprey Optimization Algorithm (OOA) and a quantitative prediction model combining Continuous Projection Algorithm (SPA) with Partial Least Squares Algorithm (PLS) were established. Qualitative analysis used eight types of microplastics, with AS, PA66, ABS, PS, POM, PBT, PET, and PVC as experimental samples. Initially, spectral data is obtained using LIF technology and the raw spectral data is pre-processed using polynomial smoothing algorithm (SG) and moving average (MA) methods. Subsequently, factor analysis (FA) and local linear embedding (LLE) techniques are applied to dimensionality reduction and then input into the ELM model. At the same time, the ELM parameter is optimized by using OOA algorithm. In the quantitative analysis, PA66 powder and soil are mixed in different proportions (10:0, 8:2, 5:5, 2:8, 0:10), SG and MA pre-processing are performed on the spectral data obtained by LIF technology, and SPA is used to select the spectral characteristic wavelength for the original data and the pre-processed spectral data, and then a linear regression model is established combined with PLS. In order to facilitate the comparison of data, the experimental results are reserved to 5 decimal places, the experimental results indicate that LIF technology is faster than traditional methods in extracting raw data. The convergence of the OOA-optimized ELM model is better than that of the PSO-optimized ELM model. Among all the models of qualitative analysis, SG-LLE-OOA-ELM had the best prediction effect, with mean square error (MSE) of 0.00834, coefficient of determination (R2) of 0.99841, root mean square error (RMSE) of 0.09134, and mean absolute error (MAE) of 0.07038. Among the models of quantitative analysis, the best effect is SG-SPA-PLS model with R2 of 0.99951.

Search for Optimal Parameters in the Control Structure of a Surgical System for Soft Tissue Operations Based on In Vitro Experiments on Cardiovascular Tissue

The surgical robots currently used in cardiac surgery are equipped with a remote center of motion (RCM) mechanism that enables the required spherical workspace. The dynamics model of the surgical robot’s RCM mechanism presented in this work includes a direct current (DC) motor, an optimal proportional–integral–derivative (PID) controller, and a LuGre friction model that takes into account the Stribeck effect and surface deformation. A finite element method (FEM) analysis of transients was carried out using the energy hypothesis of von Mises with an optimal input signal from the mechatronic system with a PID controller obtained using the Runge–Kutta differentiation method in the Dormand–Prince ordinary differential equations variant (ODE45). Five criteria were adopted for the objective function: the safety factor related to the stress function in the time-varying strength problem, the first natural frequency related to stiffness and the resonance phenomenon, the buckling coefficient in the statics problem related to stability, the static factor of safety, and the displacement of the operating tip. The force inputs to the dynamics model were derived from in vitro force measurements on cardiovascular tissue using a force sensor. The normality of the statistical distribution of the experimental data was confirmed using the Kolmogorov–Smirnov statistical test. The problem of multi-criteria optimization was solved using the non-sorter genetic algorithm (NSGA-II), the finite element method, and the von Mises distortion energy hypothesis. Velocity input signals for the transient dynamics model were obtained from a second in vitro experiment on cardiovascular tissue using the minimally robotic invasive surgery (MIRS) technique. An experienced cardiac surgeon conducted the experiment in a modern method using the Robin Heart Vision surgical robot, and a system of four complementary metal–oxide–semiconductor (CMOS) optical sensors and ariel performance analysis system (APAS-XP 2002) software were used to obtain the endoscopic tool trajectory signal. The trajectory signal was accurate to ±2 [mm] in relation to the adopted standard, and it was smoothed using the Savitzky–Golay (SG) polynomial smoothing, whose parameters were optimally selected using the Durbin–Watson (DW) statistical test.

A Mine Water Source Prediction Model Based on LIF Technology and BWO-ELM.

The traditional methods for identifying water sources in coal mines lack the ability to quickly detect water sources and are prone to causing secondary pollution of samples. In contrast, laser induced fluorescence (LIF) technology has been introduced for the identification of coal mine water sources due to its high sensitivity and real-time performance. However, extreme learning machine (ELM) have shortcomings in randomly selecting weights and biases. The Beluga Whale Optimization (BWO) algorithm has efficient optimization capability, global search capability, adaptability and parallelism, and can find the optimal weights and biases in a short time. The combination of LIF technology and BWO-ELM model can be applied to quickly identify the welling water source in coal mine. Select sandstone water and old goaf water from the Huainan mining area as experimental samples, and mix them in different proportions to prepare 7 mixed water samples for testing. Utilize LIF technology to obtain spectral curve images, preprocess them with polynomial smoothing algorithm (SG) and spectral multiple scattering correction (MSC), and perform dimensionality reduction using factor analysis (FA) and linear discriminant analysis (LDA) methods. Finally, construct ELM models, Long Short Term Memory (LSTM) models, BWO-ELM models, and Particle Swarm Optimization Extreme Learning Machine(PSO-ELM) models for the dimensionality reduced data. In order to improve the reliability and accuracy of the results, the experimental results were kept to 5 decimal places. From the experimental results, it can be seen that SG-LDA-BWO-ELM has the best fitting effect, with a fitting coefficient of 0.99990, a root mean square error of 0.00041, a mean square error approaching 0, and an average absolute error of 0.00021. It has the best convergence and the smallest absolute error among all models, making it the most suitable for identifying mine water inrush. It is of great significance for preventing and controlling mine water disasters and ensuring coal mine production safety.

Temporal trends of semen quality among male partners of infertile Greek couples undergoing oocyte donation cycles: a retrospective study in a single IVF center

Introduction: Temporal global trends of sperm quality remain a matter of debate. It is widely believed that exposure to endocrine disruptors during fetal life can damage testicular function, cause testicular cancer and impair reproduction. Materials and methods: This was a retrospective, cohort study using data from a single IVF center located in Thessaloniki, Greece, during the period 2004-2013; including male partners of infertile Greek women, undergoing oocyte donation treatment for the first time. Local polynomial smoothing was used to assess visually possible trends in the data. One-way ANOVA was used for the comparison of means of variables of interest between years. The Pearson Chi-squared and the Chi-squared test for trend were employed to test for the independence and trend respectively of the occurrence of concentrations <20 million/ml and the year of study. Results: A total of 1113 participants were analyzed. The mean sperm concentration increased significantly between 2004 and 2012 (39.5million/ml versus 59.1million/ml; p<0.001), but without forming a visible upward trend; the mean total motility remained statistically unchanged (56% versus 49.8%; p=0.239), as well as the percentage of sperm concentration of less than 20million/mL (23.5% versus 24.4%; p=0.249), whereas the mean of rapid progressive motile sperm decreased significantly (41.1% versus 30%; p<0.001), forming a visible downward trend. Conclusions: Sperm motility and annual percentage of oligospermic males presenting with a sperm concentration of less than 20 million/mL showed an absence of significant change and temporal trend. Rapid progressive motile sperm deteriorated significantly, revealing a visible time-related downward trend.

Comparison of Kernel Smoothing and Local Polynomial Smoothing Method in Overcoming Age Heaping

Age data plays an important role in every aspect yet there are found age misreporting. It involves digit preference that causes build up in a certain age. Digit preference in demography is called age heaping that often happens at age with 0 and 5 as the last digit. Age heaping induces poor data quality and data bias that could influence government policy making. Two indicators used to detect age heaping are Whipple Index (WI) and Myers Blended Index (MBI). Methods to cope with age heaping are nonparametric regression approaches which are Kernel Smoothing and Local Polynomial Smoothing. The objective of this research is to measure and elevate the quality of population age data and population mortality data in Sensus Penduduk (SP) 2020 as well as comparing methods between Kernel Smoothing and Local Polynomial Smoothing. The data being used in this paper is SP2020 which the research variables are age population, age of death, and total population. The result shows that the data quality of total population death is inaccurate compared to total population thus needs a smoothing process to improve age data to population data accuration. The method that has better accuracy is the Local Polynomial Smoothing method.

Volumetric and acoustic studies of binary mixtures of DEC with isomeric chlorobenzene at various temperatures

ABSTRACT Densities, ρ, and speeds of sound, u, of binary liquid mixtures of diethyl carbonate with 1,2-dichlorobenzene, 1,3-dichlorobenzene and 1,2,4-trichlorobenzene have been measured over the entire range of composition at 303.15 K, 308.15 K, 313.15 K and 318.15 K and at atmospheric pressure. From the experimental data of the density and speed of sound, the excess properties such as excess molar volume, V m E , excess isentropic compressibility, κ s E , excess molar isentropic compressibility, K s , m E , excess speed of sound, u E , and excess isobaric thermal expansion, α p E , have been calculated. For better knowledge of the solute and solvent interaction, excess partial molar volumes, V ˉ m , 1 E and V ˉ m , 2 E , and excess partial molar volumes, V ˉ m , 1 ∘ E and V ˉ m , 2 ∘ E of the components at infinite dilution have been measured. All the excess parameter values have been fitted using the Redlich–Kister polynomial smoothing equation. The calculated excess values have been analysed in terms of molecular interactions and structural effects.

Predicted effects of image acquisition and analysis conditions on DTMRI tractography-based muscle architecture estimates.

To quantify the effects of the intrinsic signal pattern, image acquisition conditions, and data analysis conditions on diffusion-tensor MRI (DTMRI) tractography-based muscle architecture estimates using a sampling-reconstruction assessment framework. Numerical models of muscles were constructed with realistic architectural properties. DTMRI signals were computed at signal-to-noise ratio (SNR) of 24-96 and common voxel sizes. Fiber tracking was performed, and the results were compared with the known architectural properties. SNR exerted the most significant impact on the outcome. The outcome variables approached asymptotes at SNR ≈ 54. Large in-plane voxel dimensions reduced the similarity between reconstructed fibers and the known architectural properties. Higher order polynomials helped reconstruct fibers with more complicated geometry but overfit noise for less complex geometries. The intrinsic fiber curvature also affected the robustness of polynomial smoothing to SNR. Other conditions, such as the fiber dimensionality, voxel aspect ratio, and slice thickness, did not affect the outcomes. SNR ≥ 54 is recommended for accurate muscle architecture characterization using DTMRI. Averaged across all simulated conditions, the greatest percent errors under SNR = 54 were -5.6% and -4.0% for the pennation angle and fiber-tract length estimates, respectively. For fiber tracts with intermediate intrinsic curvature, the greatest percent error for the curvature estimate was 9.8% for SNR = 54. Smaller in-plane voxel size (≤1.5 mm) is preferred to minimize the estimation error in architectural properties. If necessary, slice thickness may be adjusted within typical ranges to achieve sufficient SNR when slices are aligned near the fiber direction. Third-order polynomial fitting is appropriate for smoothing fiber tracts.

Eleven-month SARS-CoV-2 binding antibody decay, and associated factors, among mRNA vaccinees: implications for booster vaccination

Background. We examined the 11 month longitudinal antibody decay among two-dose mRNA vaccinees, and identified factors associated with faster decay. Methods. The study included samples from the COVID-19 Occupational Risk, Seroprevalence and Immunity among Paramedics (CORSIP) longitudinal observational study of paramedics in Canada. Participants were included if they had received two mRNA vaccines without prior SARS-CoV-2 infection and provided two blood samples post-vaccination. The outcomes of interest were quantitative SARS-CoV-2 antibody concentrations. We employed spaghetti and scatter plots (with kernel-weighted local polynomial smoothing curve) to describe the trend of the antibody decay over 11 months post-vaccine and fit a mixed effect exponential decay model to examine the loss of immunogenicity and factors associated with antibody waning over time. Results. This analysis included 652 blood samples from 326 adult paramedics. Total anti-spike antibody levels peaked on the twenty-first day (antibody level 9042 U ml−1) after the second mRNA vaccine dose. Total anti-spike antibody levels declined thereafter, with a half-life of 94 [95 % CI: 70, 143] days, with levels plateauing at 295 days (antibody level 1021 U ml−1). Older age, vaccine dosing interval <35 days, and the BNT162b2 vaccine (compared to mRNA-1273 vaccine) were associated with faster antibody decay. Conclusion. Antibody levels declined after the initial mRNA series with a half-life of 94 days, plateauing at 295 days. These findings may inform the timing of booster vaccine doses and identifying individuals with faster antibody decay.

Trends and long-term variation explaining nutritional determinants of child linear growth: analysis of Bangladesh Demographic and Health Surveys 1996-2018.

To examine the height-for-age z-score (HAZ) of 0-35 months' children along with stunting prevalence to identify trends, changes and available nutrition-sensitive and specific determinants that could help explain the long-term variation in child linear growth using successive Bangladesh Demographic and Health Surveys (BDHS) data from 1996 to 2018. The BDHS pooled data are used for determining the key outcome variables HAZ, stunting and severe stunting. Trends, kernel-weighted local polynomial smoothing illustrations, pooled multivariable linear probability model (LPM), ordinary least squares method (OLS) and regression decomposition were used. Mothers having 0-35 months' children, the most critical age range for growth faltering. The mean HAZ increased by 0·91(±1·53) with 0·041 annual average change, while the percentages of stunting (-26·63 ± 0·54) and severe stunting (-21·12 ± 0·48) showed a reduction with 1·21 and 0·96 average annual changes, respectively. The average HAZ improvement (0·42 ± 1·56) in urban areas was less than the rural areas (1·16 ± 1·44). Similar patterns followed for stunting and severe stunting. The prenatal doctor visits (3064·65 %), birth in a medical facility (1054·32 %), breastfeeding initiation (153·18 %) and asset index (144·73 %) demonstrated a huge change. The findings of OLS, LPM and regression decomposition identified asset index, birth order, paternal and maternal education, bottle-fed, prenatal doctor visit, birth in a medical facility, vaccination, maternal BMI and ever-breastfed as influencing factors to predict the long-term changes of stunting and severe stunting. The nutrition-sensitive and specific factors identified through regression decomposition describing long-term variation in child linear growth should be focused further to attain the sustainable development goals.

Sociodemographic features associated with the MoCA, SPPB, and GDS scores in a community-dwelling elderly population

BackgroundAn accurate evaluation of cognitive function, physical health, and psychological health is fundamental for assessing health problems in the elderly population, and it is important to identify the necessity of early therapeutic intervention. The objective of this study was to evaluate the states of mental and physical functions and to investigate the relationships between sociodemographic features and these functions in a community-dwelling elderly population.MethodsThis community-based cross-sectional study was conducted in a suburban district of Shanghai, China. A total of 1025 participants aged 60–89 years underwent investigations of demographic and lifestyle features and a multidimensional geriatric evaluation comprising the Montreal Cognitive Assessment (MoCA), Short Physical Performance Battery (SPPB), and Geriatric Depression Scale (GDS).ResultsThe results of the multivariate linear regression models demonstrated that the MoCA and SPPB scores decreased with advancing age (all P < 0.01). However, the GDS score did not exhibit an age-related decrease (P = 0.09). Both sex and living alone influenced the MoCA score (P < 0.01 and P = 0.04, respectively), SPPB score (P < 0.01 and P = 0.04, respectively), and GDS score (P < 0.01 and P < 0.01, respectively). A higher education level was related to better MoCA and SPPB scores (all P < 0.01). Furthermore, age and sex had interactive effects on the MoCA score (P = 0.03) and SPPB score (P < 0.01). The kernel-weighted local polynomial smoothing curves exhibited similar trends.ConclusionsIt is imperative to develop a more sensitive evaluation of physical function, and to encourage various intellectually and emotionally stimulating social activity strategies to promote healthy aging, especially in elderly women and those living alone who have a low education level.

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Planning an achievable trajectory for a mobile robot usually consists of two steps: (i) finding a path in the form of a sequence of discrete waypoints and (ii) transforming this sequence into a continuous and smooth curve. To solve the second problem, this paper proposes algorithms for automatic dynamic smoothing of the primary path using a tracking differentiator with sigmoid corrective actions. Algorithms for setting the gains of the differentiator are developed, considering a set of design constraints on velocity, acceleration, and jerk for various mobile robots. When tracking a non-smooth primary path, the output variables of the differentiator generate smooth trajectories implemented by a mechanical plant. It is shown that the tracking differentiator with a different number of blocks also generates derivatives of the smoothed trajectory of any required order, taking into account the given constraints. Unlike standard analytical methods of polynomial smoothing, the proposed algorithm has a low computational load. It is easily implemented in real time on the on-board computer. In addition, simple methods for modeling a safety corridor are proposed, taking into account the dimensions of the vehicle when planning a polygon with stationary obstacles. Confirming results of numerical simulation of the developed algorithms are presented.

Identifying Multi-Scale Gravity and Magnetic Anomalies Using Statistical Empirical Mode Decomposition: A Case Study from the Eastern Tianshan Orogenic Belt

Identifying multi-scale anomalies that have simple forms and geological significance is critical for enhancing the interpretability of gravity and magnetic survey data. In recent years, empirical mode decomposition (EMD), which was developed as a significant data-driven approach for analyzing complex signals, has been widely used in identifying gravity and magnetic anomalies due to its advantages of adaptability to nonlinear and nonstationary data. Nevertheless, the traditional EMD method is usually sensitive to outliers and irregularly spaced data because of the interpolation process in the construction of envelopes. In this regard, an extended algorithm called statistical EMD (SEMD) has been proposed based on the smoothing technique. In this study, for validation purposes, the novel SEMD method has been employed to identify multi-scale gravity and magnetic anomalies. The sensitivities of local polynomial and cubic spline smoothing methods in SEMD to combination and arrangement patterns of field sources including the size, depth, and distance in gravity and magnetic anomaly identification were investigated and compared by forward modeling under the same conditions. The results demonstrated that the local polynomial smoothing method performed better than the cubic spline smoothing method. Thus, in the case study, the SEMD method using the local polynomial smoothing technique was employed for identifying multi-scale gravity and magnetic anomalies in the eastern Tianshan orogenic belt, northwestern China. It has illustrated that the SEMD method provides a novel and useful data-driven method for extracting gravity and magnetic anomalies.

Optimal polynomial smoothers for multigrid V‐cycles

AbstractThe idea of using polynomial methods to improve simple smoother iterations within a multigrid method for a symmetric positive definite system is revisited. A two‐level bound going back to Hackbusch is optimized by a very simple iteration, a close cousin of the Chebyshev semi‐iterative method, but based on the Chebyshev polynomials of the fourth instead of first kind. A full V‐cycle bound for general polynomial smoothers is derived using the V‐cycle theory of McCormick. The fourth‐kind Chebyshev iteration is quasi‐optimal for the V‐cycle bound. The optimal polynomials for the V‐cycle bound can be found numerically, achieving about an 18% lower error contraction factor bound than the fourth‐kind Chebyshev iteration, asymptotically as the number of smoothing steps . Implementation of the optimized iteration is discussed, and the performance of the polynomial smoothers is illustrated with numerical examples.

Robust Transformations for Multiple Regression via Additivity and Variance Stabilization

ABSTRACT Outliers can have a major effect on the estimated transformation of the response in linear regression models, as they can on the estimates of the coefficients of the fitted model. The effect is more extreme in the Generalized Additive Models (GAMs) that are the subject of this article, as the forms of terms in the model can also be affected. We develop, describe and illustrate robust methods for the nonparametric transformation of the response and estimation of the terms in the model. Numerical integration is used to calculate the estimated variance stabilizing transformation. Robust regression provides outlier free input to the polynomial smoothers used in the calculation of the response transformation and in the backfitting algorithm for estimation of the functions of the GAM. Our starting point was the AVAS (Additivity and VAriance Stabilization) algorithm of Tibshirani. Even if robustness is not required, we have made four further general optional improvements to AVAS which greatly improve the performance of Tibshirani’s original Fortran program. We provide a publicly available and fully documented interactive program for our procedure which is a robust form of Tibshirani’s AVAS that allows many forms of robust regression. We illustrate the efficacy of our procedure through data analyses. A refinement of the backfitting algorithm has interesting implications for robust model selection. Supplementary materials for this article are available online.

(118) The Atherosclerotic Cardiovascular Disease Risk Score is a Reliable Tool to Identify Patients with Arteriogenic Erectile Dysfunction at Dynamic Penile Color Doppler Duplex Ultrasound – Findings From a Real-life Cross-sectional Study

Abstract Introduction The ASCVD (Atherosclerotic Cardiovascular Disease) risk score is a validated and standardised algorithm predicting the individual 10-year risk of developing acute cardiovascular events (CVs). Patients with erectile dysfunction (ED) are at greater risk of CVs; Objective we aimed to i) apply the ASCVD score at a homogenous cohort of men undergoing dynamic penile color doppler duplex ultrasound (CDDU) for ED, and ii) explore its predictive ability to identify patients with arteriogenic and venogenic ED at CDDU. Methods Complete data of 188 consecutive patients undergoing CDDU for ED were analysed. Health-significant comorbidities were scored using the Charlson comorbidity index. All patients completed the International Index of Erectile Function (IIEF) at baseline. Serum hormones (total testosterone (tT) and luteinising hormone (LH)) were dosed for every patient. The ASCVD score was applied to the entire cohort. According to the ASCVD, patients were segregated into low (≤7.5%) vs. intermediate/high risk (&amp;gt; 7.5%). Descriptive statistics was used to explore differences between the two groups. Logistic regression models tested the potential predictive role of ASCVD scores to predict pathological CDDU parameters (peak systolic velocity (PSV) &amp;lt; 35 cm/s and/or resistance index (RI) ≤ 0.70). Local polynomial smoothing models graphically displayed the probability of pathological CDDU parameters at different ASCVD scores. Results Overall, median (IQR) age was 54 (43-60) yr. Of all, 52 (27.7%) patients reported severe ED, as for IIEF-EF ≤ 11. Overall, 80 (42.6%) showed a pure arteriogenic ED and 15 (8%) pure venogenic ED at CDDU. Intermediate/high-risk patients (52.7%) were found to have lower IIEF-EF scores, higher BMI, higher CCI and presented with a greater rate of PDE5i non-responders compared to those with low-risk (47.3%) according to ASCVD (all p&amp;lt;0.005). Conversely, the two groups did not significantly differ in terms of CDDU parameters. At logistic regression analysis, the ASCVD risk score was identified as a strong predictor for arteriogenic ED at CDDU (OR: 1.07, 95% CI: 1.03-1.13, p = 0.007) after adjusting for BMI. Conversely, the ASCVD score was not identified as a predictor of pure venogenic ED (OR: 1.04, 95% CI: 0.98-1.1, p = 0.22). Figure 1 displays the probability of pathological findings at CDDU (PSV &amp;lt; 35 cm/sec vs. RI &amp;lt; 0.7) at different ASCVD scores. Conclusions The ASCVD risk score can be used as a valuable tool to identify patients with arteriogenic ED at CDDU in real-life settings. Since vasculogenic ED may anticipate CVs even by some years, the accurate identification of patients with deficient cavernosal arterial flow would certainly allow earlier and more effective cardiovascular prevention in this subset of patients. Disclosure No