Estimation Of Function Research Articles

The utility of split function testing in determining recovery of glomerular filtration rate after living kidney donation: a cohort study

BackgroundA number of UK transplantation centres use isotope studies to estimate the relative contribution from each kidney in living kidney donor assessment. The evidence that the estimation of pre-donation split function of the non-donated kidney influences post-donation renal recovery is limited. The aim of this study was to analyse whether, in the context of other donor factors, the split function of the non-donated kidney predicts the percentage recovery of glomerular filtration rate (GFR) at one-year post-donation.MethodologyA retrospective cohort analysis was undertaken on 291 living kidney donors in the Glasgow Renal and Transplant Unit between 1st January 2011 and 1st June 2022. Univariable and multivariable linear regression analysis was used to analyse the impact of donor factors on recovery of renal function at one year relative to baseline isotope GFR (iGFR) or to estimated GFR (eGFR by Chronic Kidney Disease Epidemiology Collaboration [CKD-EPI] formula). Sub-analyses of donor outcome (% recovery of iGFR and eGFR at one year) were undertaken using single-measures ANOVA and grouping of donors by pre-donation isotope uptake of the non-donated kidney. ResultsMedian recovery of pre-donation GFR at 1 year was 70.0% (IQR 64.8-75.5). On linear regression analysis there was no significant association found between split function of the non-donated kidney and the percentage recovery of iGFR, although a small significant association was found for eGFR. There was no significant difference between mean iGFR or eGFR recovery on sub-analysis of donor outcomes.ConclusionsThis study demonstrated no clinically important predictive relationship between percentage recovery of renal function at 1 year after living kidney donation and pre-donation split function within the range accepted for donation in our centre.

The Economic Value of the Protective Functions of Mountain Forests: A Case Study in the Italian Alps

ABSTRACT Mountain forests perform an indirect protective function against natural events. The aim of this study is to develop a method of economic valuation of the role of mountain forests in reducing the risk of windthrow and soil erosion, taking as a case study the Cansiglio Orientale forest (Italian Alps). Protection against windthrow was investigated through the slenderness coefficient, while the soil erosion protection was analysed using a model that takes into account stand and site characteristics. The risk mitigation cost method has been applied for the economic estimation of the protective functions. The main results showed that more than 63% of trees are included in areas with high stand stability, while over 54% of the area is classified as low risk of soil erosion. Finally, an economic value of € 61.72 ha−1 yr−1 – € 20.36 ha−1 yr−1 to maintain the stand stability and of € 4.39 ha−1 yr−1 – € 1.31 ha−1 yr−1 to restore soil fertility after erosion were estimated. This study has provided an approach for the economic valuation of the protective function of mountain forests based on mitigation cost method. This contribution fits into the literature concerning the economic valuation of ecosystem services to improve decision-making process.

Estimation of factorial expressions and its improvement through calibration: A replication and extension of Tversky and Kahneman (1973).

Fifty years ago, Tversky and Kahneman (Cognitive Psychology, 5[2], 207-232, 1973) reported that people's speeded estimations of 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 were notably higher than their estimations for the equivalent expression in the opposite order, 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 (Median = 2,250 vs. 512, respectively). On top of this order effect, both groups grossly underestimated the correct value (40,320). The differential effect of the two orders on estimation has become famous as an early demonstration of the anchoring effect, where people's judgments under uncertainty are unduly influenced by an initial reference point (or "anchor"). Despite this fame, to the best of our knowledge, this effect has never been replicated. In a sample of 253 U.S. adults, the current study provides the first replication of this foundational example of anchoring. It extends this effect for the first time to a within-participants design, revealing its relative robustness even among participants who see the descending order first. Drawing on procedures from the mathematical cognition literature, it shows how the anchoring effect can be mitigated: calibrating to the correct value of 6! reduces this effect, and calibrating to 10! eliminates it altogether. An individual differences analysis measures the arithmetic fluency of participants and their accuracy on a new estimation assessment, and finds that higher estimation ability may be a "protective factor" against some anchoring effects. These findings affirm the anchoring effect of Tversky and Kahneman (1973, Study 6) while suggesting that calibration may be an effective strategy for helping to improve people's estimation of superlinear functions that are important in real-life contexts.

DEVELOPMENT OF NONPARAMETRIC PATH FUNCTION USING HYBRID TRUNCATED SPLINE AND KERNEL FOR MODELING WASTE-TO-ECONOMIC VALUE BEHAVIOR

Waste management remains a challenge, including in Batu City, East Java, Indonesia. Rapid population growth and economic activities in the city have resulted in a substantial increase in waste volume. One of the key factors in solving waste problems is the mindset of the community towards waste management. The application of statistical analysis methods can be an effective approach to solving problems related to waste management from an economic point of view. Nonparametric path analysis is a statistical method that does not rely on the assumption that the curve is known. Nonparametric path analysis is performed if the data does not fulfill the linearity assumption. This study aims to determine the best nonparametric path function with a hybrid truncated spline and kernel approach among EV values of 0.5; 0.8; and 1. In addition, this study also aims to test the significance of the best path function obtained. The data used in this study are timer data obtained from the Featured Basic Research Grant. The results showed that the best model of hybrid truncated spline and kernel nonparametric path analysis is a hybrid model of truncated spline nonparametric path of linear polynomial degree 1 knot and kernel triangle nonparametric path at EV 0.5. In addition, the significance of the best nonparametric truncated spline and kernel hybrid path function estimation using jackknife resampling shows that all exogenous variables have a significant effect on endogenous variables as evidenced by a p-value smaller than (0.05).

The added value of metadata on test completion time for the quantification of cognitive functioning in survey research.

Information on the time spent completing cognitive testing is often collected, but such data are not typically considered when quantifying cognition in large-scale community-based surveys. We sought to evaluate the added value of timing data over and above traditional cognitive scores for the measurement of cognition in older adults. We used data from the Longitudinal Aging Study in India-Diagnostic Assessment of Dementia (LASI-DAD) study (N = 4,091), to assess the added value of timing data over and above traditional cognitive scores, using item-specific regression models for 36 cognitive test items. Models were adjusted for age, gender, interviewer, and item score. Compared to Quintile 3 (median time), taking longer to complete specific items was associated (p < 0.05) with lower cognitive performance for 67% (Quintile 5) and 28% (Quintile 4) of items. Responding quickly (Quintile 1) was associated with higher cognitive performance for 25% of simpler items (e.g., orientation for year), but with lower cognitive functioning for 63% of items requiring higher-order processing (e.g., digit span test). Results were consistent in a range of different analyses adjusting for factors including education, hearing impairment, and language of administration and in models using splines rather than quintiles. Response times from cognitive testing may contain important information on cognition not captured in traditional scoring. Incorporation of this information has the potential to improve existing estimates of cognitive functioning.

Nonparametric Time Varying IV-SVARs: Estimation and Inference

This paper studies the estimation and inference of time-varying impulse response functions in structural vector autoregressions (SVARs) identified with external instruments. Building on kernel estimators that allow for nonparametric time variation, we derive the asymptotic distributions of the relevant quantities. Our estimators are simple and computationally trivial and allow for potentially weak instruments. Simulations suggest satisfactory empirical coverage even in relatively small samples as long as the underlying parameter instabilities are sufficiently smooth. We illustrate the methods by studying the time-varying effects of global oil supply news shocks on US industrial production.

Plasma neutrophil gelatinase-associated lipocalin as a single test rule out biomarker for acute kidney injury: A cross-sectional study in patients admitted to the emergency department.

Acute kidney injury (AKI) is a syndrome with high mortality and morbidity in part due to delayed recognition based on changes in creatinine. A marker for AKI based on a single measurement is needed and therefore the performance of a single measurement of plasma neutrophil gelatinase-associated lipocalin (pNGAL) to predict AKI in patients admitted to the emergency department was tested. Samples from the Triage study which included 6005 consecutive adult patients admitted to the emergency department were tested for pNGAL. The optimal cutoff for pNGAL was determined by the AUC and compared to AKI based on creatinine using different estimations of the premorbid kidney function. In 4833 patients, two or more plasma creatinine (pCr) measurements were available allowing the detection of AKI. The highest prevalence of AKI (10%) was found when defining AKI as an increase in pCr ≥26.5 μmol/L from the prior year's mean pCr. At these conditions the AUC for pNGAL to predict AKI was 85% giving an optimal cutoff of 142.5 ng/mL with a negative predictive value of 0.96, a positive predictive value of 0.35, a specificity of 0.87 and a sensitivity of 0.70. The study illustrates that the value of a single measurement of pNGAL is primarily in excluding AKI whereas it`s poorer in predicting the presence of AKI. When diagnosing AKI with pCr the optimal baseline pCr level is the mean of available pCr (mb-pCr) measurements from up to a year prior to the current event.

Model-free robust reinforcement learning via Polynomial Chaos

In recent years, the Robust Markov Decision Process (RMDP) has become an important modeling framework to address the discrepancies between simulated and real-world environments in Reinforcement Learning (RL) training. The purpose of RMDP is to accommodate the uncertainty of the real-world environments, employing a conservative approach to enhance the robustness of policy decisions. However, due to the difficulty of robust value function estimation, the RMDP framework is challenging to generalize to environments with large continuous state–action spaces. Our work focuses on model-free robust RL and proposes a model-free algorithm for continuous space setting. We adopt a new perspective on uncertainty sets such that the uncertainty sets are parameterized and the parameters obey specific stochastic distributions. We present a novel approach RPC to estimate the robust value function utilizing generalized Polynomial Chaos(gPC). We provide a proof to guarantee the convergence of the algorithm. Our training framework is based on off-policy RL, which reduces the computation overhead by gPC and improves learning stability. Our algorithm can handle continuous tasks and guarantee the robustness of the algorithm without incurring excessive computational overhead. We combine RPC with the TD3 method and conduct several experiments to evaluate its performance in a continuous robot control task, and the experimental results provide further evidence of the robustness of our algorithm.

Strong law for randomly weighted sums of WOD random variables and application to nonparametric regression models

This paper is devoted to the strong law for randomly weighted sums random variables. First, based on the properties of slowly varying functions and the de Bruijn conjugates, we prove a general result on the Marcinkiewicz-Zygmund strong law of large numbers for randomly weighted sums of widely orthant dependent (WOD, in short) random variables with general norming constants. In the second part of this paper, we establish almost sure consistency and convergence rate for the estimator of nonparametric regression model based on widely orthant dependent errors. The simulations to study the numerical performance of the consistency for the nearest neighbour weight function estimator are given to support the theoretical results.

CLASSES OF CLOSE-TO-STARLIKE FUNCTIONS BASED ON THE REFERENCE FUNCTION OF A GENERAL FORM

The purpose of the article is to introduce and explore a wide class of doubly close-to-starlike functions, while demonstrating a unified approach to solving a certain range of extreme problems. The article defines a reference function of a general form – a starlike function, on the basis of which classes of close-to-starlike and doubly close-to-starlike functions can be constructed. On the basis of a general support function containing three parameters and new estimates of analytical functions, a generalization of various classes of close-to-starlike and doubly close-to-starlike functions is introduced, considered in a number of articles published in recent years, including the introduced class contains a generalized class of typically real functions. The properties of the introduced class of functions are studied, for example, the growth theorem, estimates of the modulus of the logarithmic derivative of the function and the radius of starlikeness are obtained, in particular cases leading to previously known results and representing new results. All the results of the article are accurate.

Calibrated Equilibrium Estimation and Double Selection for High-dimensional Partially Linear Measurement Error Models

In practice, measurement error data is frequently encountered and needs to be handled appropriately. As a result of additional bias induced by measurement error, many existing estimation methods fail to achieve satisfactory performances. This article studies high-dimensional partially linear measurement error models. It proposes a calibrated equilibrium (CARE) estimation method to calibrate the bias caused by measurement error and overcomes the technical difficulty of the objective function unbounded from below in high-dimensional cases due to non-convexity. To facilitate the applications of the CARE estimation method, a bootstrap approach for approximating the covariance matrix of measurement errors is introduced. For the high-dimensional or ultra-high dimensional partially linear measurement error models, a novel multiple testing method, the calibrated equilibrium multiple double selection (CARE–MUSE) algorithm, is proposed to control the false discovery rate (FDR). Under certain regularity conditions, we derive the oracle inequalities for estimation error and prediction risk, along with an upper bound on the number of falsely discovered signs for the CARE estimator. We further establish the convergence rate of the nonparametric function estimator. In addition, FDR and power guarantee for the CARE–MUSE algorithm are investigated under a weaker minimum signal condition, which is insufficient for the CARE estimator to achieve sign consistency. Extensive simulation studies and a real data application demonstrate the satisfactory finite sample performance of the proposed methods.

Maximum Penalized-Likelihood Structured Covariance Estimation for Imaging Extended Objects, with Application to Radio Astronomy

Image formation in radio astronomy is often posed as a problem of constructing a nonnegative function from sparse samples of its Fourier transform. We explore an alternative approach that reformulates the problem in terms of estimating the entries of a diagonal covariance matrix from Gaussian data. Maximum-likelihood estimates of the covariance cannot be readily computed analytically; hence, we investigate an iterative algorithm originally proposed by Snyder, O’Sullivan, and Miller in the context of radar imaging. The resulting maximum-likelihood estimates tend to be unacceptably rough due to the ill-posed nature of the maximum-likelihood estimation of functions from limited data, so some kind of regularization is needed. We explore penalized likelihoods based on entropy functionals, a roughness penalty proposed by Silverman, and an information-theoretic formulation of Good’s roughness penalty crafted by O’Sullivan. We also investigate algorithm variations that perform a generic smoothing step at each iteration. The results illustrate that tuning parameters allow for a tradeoff between the noise and blurriness of the reconstruction.

Analysis of Variance of Tensor Product Reproducing Kernel Hilbert Spaces on Metric Spaces

Many methods have been developed to analyze complex data, such as non-Euclidean shape, network, and manifold data. However, there is a lack of methods for studying interactions among complex data. In this paper, we first propose a novel kernel function for a metric space and construct its associated reproducing kernel Hilbert space. The new nonstationary kernel function provides a flexible and powerful tool for learning complex structures in non-Euclidean data. We then construct an analysis of variance (ANOVA) decomposition of the nonparametric regression function defined on metric space, which provides a hierarchical structure for investigating the main effects and interactions. We develop estimation and computational methods for a semi-parametric model with a multivariate function on a product of metric spaces modeled by the ANOVA decomposition. We establish the convergence rates of parameter and nonparametric function estimates. The application of the proposed methods to the Alzheimer’s Disease Neuroimaging Initiative hippocampus shape data confirms some existing and suggests some new interactions among hippocampal regions. Simulations indicate that the proposed methods work well.

A POSTERIORI ERROR ESTIMATES FOR APPROXIMATE SOLUTIONS OF THE OBSTACLE PROBLEM FOR THE 𝑝-LAPLACIAN

The paper is concerned with a functional identity and estimates which are fulfilled for the measures of deviations from exact solutions of the obstacle problem for the 𝑝-Laplacian. They hold true for any functions from the corresponding (energy) functional class, which contains the generalised solution of the problem as well. We do not use any special properties of approximations or numerical methods nor information of the exact configuration of the coincidence set. The right-hand side of the identities and estimates contains only known functions and can be explicitly calculated, and the left side represents a certain measure of the deviation of the approximate solution from the exact solution. The right-hand side of the identity and estimates contains only known functions and can be explicitly calculated, while and the left side represents a certain measure of the deviation of the approximate solution from the exact one. The obtained functional relations allow to estimate the error of of any approximate solutions of the problem regardless of the method of their obtaining. In addition, they enable to compare the exact solutions of problems with different data. The latter provides the possibility to estimate the errors of mathematical models.

Pupillometric and perceptual approaches provide independent estimates of melanopsin activity in humans.

Melanopsin-expressing retinal ganglion cells, which provide light information to time sleep and entrain circadian clocks, also influence perceived brightness raising the possibility that psychophysical paradigms could be used to explore the origins and implications of variability in melanopic sensitivity. We aimed to develop accessible psychophysical tests of melanopic vision and relate outcomes with a pupillometric measure of melanopsin function (post-illumination pupil response; PIPR) and prior light exposure. Individually calibrated pairs of isoluminant stimuli differing in melanopic radiance from a four primary source were presented sequentially with superimposed random colour offsets in a two alternative forced choice brightness preference paradigm to 41 naïve adult participants with personal light exposure data for the prior 7 days and PIPR measures defined by comparing maintained pupil constriction for luminance matched 'red' vs 'blue' pulses. Across participants we observed the expected tendency to report positive melanopsin contrast stimuli as 'brighter' (one-tailed t-test p<0.001), but with substantial inter-individual variability in both sensitivity (melanopsin contrast at criterion preference p=0.75) and amplitude (preference at maximum melanopic contrast). There was little correlation between these psychophysical outcomes and PIPR magnitude, or between either psychophysical or PIPR measures and light history metrics (pairwise Pearson correlation coefficients -0.5> <0.5). Random forest machine learning failed to satisfactorily predict outcome for either psychophysical or PIPR measures based upon these inputs. Our findings reveal that estimates of melanopic function provided by perceptual and pupillometric paradigms can be largely independent of one another and of recent history of light exposure.

Solvability of the Lp Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph

We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is parabolic A∞ with respect to surface measure (which property is in turn equivalent to Lp solvability of the Dirichlet problem for some finite p), then the function defining the graph has a half-order time derivative in the space of (parabolic) bounded mean oscillation. Equivalently, we prove that the A∞ property of caloric measure implies, in this case, that the boundary is parabolic uniformly rectifiable. Consequently, by combining our result with the work of Lewis and Murray we resolve a long standing open problem in the field by characterizing those parabolic Lipschitz graph domains for which one has Lp solvability (for some p<∞) of the Dirichlet problem for the heat equation. The key idea of our proof is to view the level sets of the Green function as extensions of the original boundary graph for which we can prove (local) square function estimates of Littlewood-Paley type.

Moving Set Size Ranked Set Sampling

A new variation of ranked set sampling technique, entitled &amp;quot;Moving set size ranked set sampling&amp;quot;, (MSSRSS), is suggested. The suggested variation allows for the increase of the number of units that can be chosen by judgement. The suitability of this modified technique for the estimation of parameters of the underlying distribution of interest is investigated. In addition, the estimation of the cumulative distribution function using this variation is considered. The results indicate that this modified technique can be useful in practice.

Modeling Nonlinear Effects in Risk Ratio and Risk Difference Using Poisson and Gaussian Additive Regression Models

The logistic additive regression model has been a standard method in modeling nonlinear effects for multivariate analyses of binary outcomes in the generalized additive model (GAM) framework. However, the resultant nonlinear estimate of the smooth function is interpreted as a nonproportional increment of the odds ratio in the increment of the explanatory variable. The odds ratio cannot be interpreted as an effect measure by itself; it is only interpretable as an approximation of the risk ratio when the frequency of events is low. In this article, we propose alternative nonlinear regression methods to estimate the risk ratio and risk difference directly. We propose extending Zou’s modified Poisson regression (Am J Epidemiol 159: 702–6) and Cheung’s modified least squares (Gaussian) regression (Am J Epidemiol 166: 1337–44) to the GAM framework and fitting the Poisson and Gaussian additive regression models to binary outcome data. We show that valid nonlinear effects estimates are obtained using these approaches and that they can be easily implemented using existing GAM statistical packages. We also provide valid computational methods for obtaining the standard errors and confidence intervals using a bootstrap method. We illustrate these proposed methods through applications to a breast cancer clinical study.

The Analysis of Parameters Affecting Indoor Air Pollution and Noise Levels Under the Applied Theory of Covariance Functions

Analysis variations in the intensity of vectors estimating indoor air pollution (PM2.5, PM10 and CO2) and noise levels are presented. The research was conducted in an office room during COVID-19. The theory of covariance functions was used to analyse changes in the intensity of the vectors of determined parameters. The estimates of the cross-covariance functions of digital vectors and the autocovariance functions of the individual vectors of air pollution and noise recording sensor parameters were calculated in line with the random functions of data arrays measuring the vectors of air pollution sensor parameters. The approximations of covariance functions were calculated by changing the quantisation interval on a time scale and applying software created based on the Matlab procedure package. The stochastic interdependence of the vectors of air pollution and noise level recording sensor parameters and variations in vectors on the time scale was established.

Functional partial linear regression with quadratic regression for the multivariate predictor

. In the last decades, functional semi-parametric models are widely studied such as functional additive model, functional partial linear model, functional index model, and so on. But some of the semi-parametric models suffer from the lower convergence rate for the non parametric parts (especially for the non parametric functional regression) and the assumption for the linear parts is too strict in practical. In this article, we propose a functional partial linear model corresponding to a scalar response, while the predictors contain both of function and multivariate predictor. We use a functional linear model to avoid the low convergence rate of the non parametric functional estimation, and for the multivariate predictor, we use a quadratic regression model to deal with the strict assumption for the linear model. To estimate this model, we first expand the functional predictor and functional regression parametric on the functional principal component basis, then, we estimate the functional coefficient by the least square method. For the theoretical studying, we will study the asymptotical normal distribution of the multivariate regression parameter and the specific convergence rate of the functional regression parameter for the dense functional observations. Furthermore, we illustrate the performance of the proposed method by simulation studies and one real data analysis.