Nonparametric Regression Model Research Articles

Research on Prediction of Urban Traffic Congestion Time and Construction of Traffic System based on Survival Analysis

With the development of economy and society, the number of cars in major cities in China has been rising sharply in recent years, and the traffic congestion problem has become increasingly serious. Aiming at the prediction of traffic congestion time, multiple linear regression and survival analysis methods are used to establish multiple linear model, Kaplan-Meier nonparametric regression model, Cox regression model and other prediction models. SPSS, MATLAB and other programming software are used to make the congestion index expression, and the internal relations among the influencing variables are discussed by combining the correlation coefficient matrix. Based on this, the probability distribution of congestion time is explored, and the results obtained have certain reference significance for formulating traffic policies, improving traffic trips and achieving the urbanization development goal based on smart growth.

Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation

This article develops a sparsity-inducing version of Bayesian Causal Forests, a recently proposed nonparametric causal regression model that employs Bayesian Additive Regression Trees and is specifically designed to estimate heterogeneous treatment effects using observational data. The sparsity-inducing component we introduce is motivated by empirical studies where not all the available covariates are relevant, leading to different degrees of sparsity underlying the surfaces of interest in the estimation of individual treatment effects. The extended version presented in this work, which we name Shrinkage Bayesian Causal Forest, is equipped with an additional pair of priors allowing the model to adjust the weight of each covariate through the corresponding number of splits in the tree ensemble. These priors improve the model’s adaptability to sparse data generating processes and allow to perform fully Bayesian feature shrinkage in a framework for treatment effects estimation, and thus to uncover the moderating factors driving heterogeneity. In addition, the method allows prior knowledge about the relevant confounding covariates and the relative magnitude of their impact on the outcome to be incorporated in the model. We illustrate the performance of our method in simulated studies, in comparison to Bayesian Causal Forest and other state-of-the-art models, to demonstrate how it scales up with an increasing number of covariates and how it handles strongly confounded scenarios. Finally, we also provide an example of application using real-world data. Supplementary materials for this article are available online.

Asymptotic equivalence for nonparametric regression with dependent errors: Gauss–Markov processes

For the class of Gauss–Markov processes we study the problem of asymptotic equivalence of the nonparametric regression model with errors given by the increments of the process and the continuous time model, where a whole path of a sum of a deterministic signal and the Gauss–Markov process can be observed. We derive sufficient conditions which imply asymptotic equivalence of the two models. We verify these conditions for the special cases of Sobolev ellipsoids and Hölder classes with smoothness index \(>1/2\) under mild assumptions on the Gauss–Markov process. To give a counterexample, we show that asymptotic equivalence fails to hold for the special case of Brownian bridge. Our findings demonstrate that the well-known asymptotic equivalence of the Gaussian white noise model and the nonparametric regression model with i.i.d. standard normal errors (see Brown and Low (Ann Stat 24:2384–2398, 1996)) can be extended to a setup with general Gauss–Markov noises.

Optimal convergence rates of Bayesian wavelet estimation with a novel empirical prior in nonparametric regression model

This paper provides a novel empirical prior for Bayesian wavelet in the nonparametric regression model. The prior centres the wavelet coefficient at the individual sample observation, and we make a modification on the empirical prior by introducing a fractional power. The optimal rates of the posterior contraction and posterior mean estimator are established by the fractional likelihood method over Besov spaces. Comparison with some methods in the literature indicates that the modified empirical method is superior in terms of the mean squared error.

Association of Radiation Timing with Long-Term Satisfaction and Health-Related Quality of Life in Prosthetic Breast Reconstruction.

Radiation therapy is increasingly used after breast cancer surgery, which may impact patients' postoperative quality of life. This study assessed differences in long-term patient satisfaction and health-related quality of life after radiation therapy administered at different stages of implant-based breast reconstruction or with no radiation after surgery. In this observational study, long-term outcomes were evaluated for four cohorts of women who completed breast reconstruction and received (1) no radiation, (2) radiation before tissue expander placement, (3) radiation after tissue expander placement, or (4) radiation after permanent implant between 2010 and 2017 at Memorial Sloan Kettering. Satisfaction and health-related quality of life were assessed using the prospectively collected Satisfaction with Breasts and Physical Well-Being of Chest BREAST-Q subscales. Score distributions were examined by radiation exposure status for 3 years after surgery using nonparametric analyses and regression models. Of 2932 patients who met the inclusion criteria, 25.8 percent received radiation during breast cancer treatment, including before tissue expander placement ( n = 239; 8.2 percent), after tissue expander placement ( n = 290; 9.9 percent), and after implant placement ( n = 228; 7.8 percent). Radiotherapy patients had average scores 7 to 9 points lower at all postoperative time points for Satisfaction with Breasts and Physical Well-Being of Chest subscales ( p < 0.001). Although patient-reported outcomes did not differ by radiation timing, there were higher rates of severe capsular contracture with postimplant radiotherapy ( p < 0.001). Radiation therapy significantly affected patient satisfaction and health-related quality of life following implant breast reconstruction through 3 years postoperatively. Patient perception of outcome was unaffected by radiotherapy timing; however, capsular contracture was higher after postimplant radiotherapy, suggesting there may be an advantage to performing radiotherapy before placement of the final reconstruction. Therapeutic, III.

Multi-objective optimization of microchannel heatsink with wavy microtube by combining response surface method and genetic algorithm

This paper utilizes a combination of response surface method and genetic algorithm to provide an optimized model for microchannel heatsink with wavy microtube. The effect of flow rate in microchannel and microtube, location and diameter of microtube on the desired response surfaces, including hydrodynamic, thermal, and entropy parameters is examined. Then, the correlation between the variables is determined using a non-parametric regression model. The optimal design points are identified by multi-objective optimization and the Pareto diagram. The greatest effect is related to the nominal Reynolds number, with is directly related to the pumping power and entropy generation. The next effective parameter is the diameter of the microtube, which is inversely related to the pumping power, average surface temperature, and entropy generation. It is found that the maximum temperature difference on the hot surface is 3.1 K for optimal design HS3. For the geometry HS1, this value is less than 0.9 K by examining the optimal geometries of the micro heatsink based on the simultaneous study of the uniformity of CPU surface temperature and average CPU temperature. In addition, the flow velocity in the microtube of the design HS1 is much higher than that of the design HS3.

The Improved Nonparametric Regression Model for the IoT Link Load Balancing Control Algorithm

In order to improve the load balance control effect of the Internet of Things link, this paper combines the nonparametric regression model to improve the load balancing algorithm of the Internet of Things link. Moreover, this paper proposes a load balancing research strategy based on data plane data flow, which is aimed at improving the load balancing problem of data flow in the link. The data center network uses a multilayer fat tree topology to store information in the flow table corresponding to the switch for data flow processing and forwarding operations. In addition, this paper constructs a load balancing model for intelligent Internet of Things link and verifies the model in this paper through experimental research. The research results show that the load balancing control algorithm for Internet of Things link based on the nonparametric regression model proposed in this paper can effectively improve the internal scheduling of the Internet of Things link system and promote the load balancing effect.

Semiparametric Regression Models and Applicability in Agriculture

Parametric regression models assume that the dependent variable is a linear relationship with the independent variables and the form of the relationship is known. Nonparametric regression methods are applied in cases where the relationship type is not known or assumptions cannot be provided. However, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while some may be in a nonlinear relationship. In order to model these variables, semiparametric regression models, which are a combination of parametric and nonparametric regression methods, are used. In this study parametric, nonparametric and semiparametric regression models, parametric estimates, fit statistical values of the models, confidence intervals and standard error values were calculated. As a result of the analysis, the parameters of the milking unit and the quarantine area among the parametric variables, the operation area, the ventilation area, the number of ventilation, the quarantine area, the infirmary area, the manure pit and the distance to the center among the non-parametric variables were found to be statistically very important (P

Complete convergence for maximum of weighted sums of WNOD random variables and its application

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05.

Predictors of Quality of Life Six Years after Curative Colorectal Cancer Surgery: Results of the Prospective Multicenter Study.

Background and objectives: Improving early diagnosis and advances in colorectal cancer (CRC) treatment leads to longer survival of these patients. The purpose of this study was to identify the main surgical factors affecting long-term Quality of life (QoL) among colorectal cancer patients after surgery. Materials and Methods: QoL was prospectively evaluated in patients undergoing elective colorectal cancer resection operations in three CRC surgery centers of Lithuania using EORTC generic (QLQC-30) and disease-specific (QLQ-CR29) questionnaires at the time of preoperative admission and 1, 24, and 72 months after surgery. QoL was evaluated among different patient groups, diagnostic and treatment modalities, disease, and postoperative complications. Non-parametric tests and multivariate logistic regression models were used for statistical analysis. Results: Eighty-eight consecutive CRC patients from three institutions were included in the study over a three-month inclusion period, 42 (47.73%) women and 46 (52.27%) men, mean age 64.2 ± 11.5 years. Most tumors were localized in the sigmoid colon and rectum. The largest number of patients had stage III cancer. Twenty-nine patients died—a 6-year survival rate was 67%. 50 of 59 live patients (84.8%) responded to the questionnaire 6 years after their operation. Evaluating changes in quality of life 72 months after surgery with assessments before surgery, both questionnaire responses revealed good long-term CRC surgical treatment results: improved general and functional scale estimates and decreased symptom scale ratings. The multivariate analysis found that age, stoma formation, and rectal cancer were independent risk factors for having worse QoL six years after surgical intervention. Conclusions: Six years after surgery, QoL returns to preoperative levels. Age, stoma formation, adjuvant treatment, and rectal cancer reduce long-term QoL.

Estimation and Model Selection for Nonparametric Function-on-Function Regression

Regression models with a functional response and functional covariate have received significant attention recently. While various nonparametric and semiparametric models have been developed, there is an urgent need for model selection and diagnostic methods. In this article, we develop a unified framework for estimation and model selection in nonparametric function-on-function regression. We propose a general nonparametric functional regression model with the model space constructed through smoothing spline analysis of variance (SS ANOVA). The proposed model reduces to some of the existing models when selected components in the SS ANOVA decomposition are eliminated. We propose new estimation procedures under either L 1 or L 2 penalty and show that the combination of the SS ANOVA decomposition and L 1 penalty provides powerful tools for model selection and diagnostics. We establish consistency and convergence rates for estimates of the regression function and each component in its decomposition under both the L 1 and L 2 penalties. Simulation studies and real examples show that the proposed methods perform well. Technical details and additional simulation results are available in online supplementary materials.

Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review

Abstract Large observational data are increasingly available in disciplines such as health, economic and social sciences, where researchers are interested in causal questions rather than prediction. In this paper, we examine the problem of estimating heterogeneous treatment effects using non-parametric regression-based methods, starting from an empirical study aimed at investigating the effect of participation in school meal programs on health indicators. First, we introduce the setup and the issues related to conducting causal inference with observational or non-fully randomized data, and how these issues can be tackled with the help of statistical learning tools. Then, we review and develop a unifying taxonomy of the existing state-of-the-art frameworks that allow for individual treatment effects estimation via non-parametric regression models. After presenting a brief overview on the problem of model selection, we illustrate the performance of some of the methods on three different simulated studies. We conclude by demonstrating the use of some of the methods on an empirical analysis of the school meal program data.

The central limit theorem for ANA sequences and its application to nonparametric regression models

In the paper, the central limit theorem for asymptotically negatively associated (ANA, for short) random variables is established. As an application, we consider the nonparametric regression model with repeated measurements: , where is the jth response at the point , 's are known fixed design points, and is an unknown Borel measurable function defined on . Under some general conditions, we study the asymptotic normality of the wavelet estimator of under ANA random errors. The obtained results generalize the corresponding ones for NA random variables. Finally, we will provide the simulation study to assess the finite sample performance of the theoretical results.

Parasagittal dural space and cerebrospinal fluid (CSF) flow across the lifespan in healthy adults

BackgroundRecent studies have suggested alternative cerebrospinal fluid (CSF) clearance pathways for brain parenchymal metabolic waste products. One fundamental but relatively under-explored component of these pathways is the anatomic region surrounding the superior sagittal sinus, which has been shown to have relevance to trans-arachnoid molecular passage. This so-called parasagittal dural (PSD) space may play a physiologically significant role as a distal intracranial component of the human glymphatic circuit, yet fundamental gaps persist in our knowledge of how this space changes with normal aging and intracranial bulk fluid transport.MethodsWe re-parameterized MRI methods to assess CSF circulation in humans using high resolution imaging of the PSD space and phase contrast measures of flow through the cerebral aqueduct to test the hypotheses that volumetric measures of PSD space (1) are directly related to CSF flow (mL/s) through the cerebral aqueduct, and (2) increase with age. Multi-modal 3-Tesla MRI was applied in healthy participants (n = 62; age range = 20–83 years) across the adult lifespan whereby phase contrast assessments of CSF flow through the aqueduct were paired with non-contrasted T1-weighted and T2-weighted MRI for PSD volumetry. PSD volume was extracted using a recently validated neural networks algorithm. Non-parametric regression models were applied to evaluate how PSD volume related to tissue volume and age cross-sectionally, and separately how PSD volume related to CSF flow (significance criteria: two-sided p < 0.05).ResultsA significant PSD volume enlargement in relation to normal aging (p < 0.001, Spearman’s-rho = 0.6), CSF volume (p < 0.001, Spearman’s-rho = 0.6) and maximum CSF flow through the aqueduct of Sylvius (anterograde and retrograde, p < 0.001) were observed. The elevation in PSD volume was not significantly related to gray or white matter tissue volumes. Findings are consistent with PSD volume increasing with age and bulk CSF flow.ConclusionsFindings highlight the feasibility of quantifying PSD volume non-invasively in vivo in humans using machine learning and non-contrast MRI. Additionally, findings demonstrate that PSD volume increases with age and relates to CSF volume and bi-directional flow. Values reported should provide useful normative ranges for how PSD volume adjusts with age, which will serve as a necessary pre-requisite for comparisons to persons with neurodegenerative disorders.

Association between mobile work and work ability: a longitudinal study under the impact of the COVID-19 pandemic

ObjectiveThis study examines the effect of mobile work on work ability as direct predictor and as factor moderating workplace stressors and resources. Originally, the study focused on the effects of mobile work on work ability in a mobile test group compared to office workers. As the study period of 1 year collided with the beginning of the COVID-19 pandemic and lockdown restrictions, we can now explore the association of mobile work and work ability before and during the first year of the COVID-19 pandemic.MethodsThis longitudinal, exploratory study took place in a medium-sized company in the social insurance sector in Germany. We used a mixed-methods design (online survey and focus group interviews) with two survey dates 1 year apart (T0: summer/autumn 2019 (before COVID-19 pandemic), T1: summer 2020 (during COVID-19 pandemic, after first strict lockdown)). Quantitative data, which are reported here, were collected by means of an online questionnaire, which includes questions on mobile work and validated measures for work-related stressors and resources and work ability. Non-parametric tests, regression analysis, and logistic regression models were used for data analysis.ResultsThe linked data set of both survey dates includes N = 102 persons (men: 37%, mean age: 41–50 years). Interestingly, we found an improvement in work ability over the course of the study (p = 0.007), although it included the first and most drastic COVID-19 restrictions in Germany. Before the pandemic, correlations between work ability and work-related stressors (e.g., work–privacy conflicts) and resources (e.g., sense of community) were evident. Some of these factors are moderated by mobile work. During the COVID-19 pandemic, mobile work was identified as independent factor for work ability. In addition, technology competence conviction gained importance as a personal resource in our cohort.ConclusionsWork ability can be influenced by many factors. Our study, which allowed for a comparison of work ability before and during COVID-19 pandemic, suggests that mobile work can be especially helpful to maintain work ability in times of change. Our findings support the notion that—under normal conditions—mobile work can influence work ability via work-related stressors and resources. In times of changes, it can have an independent effect on work ability. It must be assumed that the effects can be highly individual or context-specific.

Novel deep learning approach to model and predict the spread of COVID-19

SARS-CoV2, which causes coronavirus disease (COVID-19) is continuing to spread globally, producing new variants and has become a pandemic. People have lost their lives not only due to the virus but also because of the lack of counter measures in place. Given the increasing caseload and uncertainty of spread, there is an urgent need to develop robust artificial intelligence techniques to predict the spread of COVID-19. In this paper, we propose a deep learning technique, called Deep Sequential Prediction Model (DSPM) and machine learning based Non-parametric Regression Model (NRM) to predict the spread of COVID-19. Our proposed models are trained and tested on publicly available novel coronavirus dataset. The proposed models are evaluated by using Mean Absolute Error and compared with the existing methods for the prediction of the spread of COVID-19. Our experimental results demonstrate the superior prediction performance of the proposed models. The proposed DSPM and NRM achieve MAEs of 388.43 (error rate 1.6%) and 142.23 (0.6%), respectively compared to 6508.22 (27%) achieved by baseline SVM, 891.13 (9.2%) by Time-Series Model (TSM), 615.25 (7.4%) by LSTM-based Data-Driven Estimation Method (DDEM) and 929.72 (8.1%) by Maximum-Hasting Estimation Method (MHEM).

Optimizing evaluation in pediatric and young adult patients with Marfan syndrome: Novel longitudinal metrics to track growth of aortic structures

ObjectiveSurveillance metrics in pediatric and young adult Marfan syndrome (pMFS) are challenging. We evaluated the utility of aortic root cross-sectional area/height index (CSA/Ht) on echocardiogram among pMFS patients as a risk stratification and surgical triage metric. MethodsGenotype or phenotype positive pMFS patients aged 25 years or younger seen at our center from 2001 to 2020 were identified. Time-related transition to surgery was modeled using parametric methods. Predictive utility of CSA/Ht compared with aortic root diameter (ARd) and root Z score (ARz) were modeled using nonlinear multivariable parametric and nonparametric longitudinal regression models. ResultsSeventy-nine patients (43% female) presented at median age of 5.8 years (15th-85th percentile, 0.75-17 years) with median follow-up of 4.4 years (range, 0-18.5 years). Baseline echocardiography data were: CSA/Ht, 3.9 ± 1.4 cm2/m; ARd, 2.4 ± 0.89 cm; and ARz, 2.4 ± 1.7. CSA/Ht tracked ARd better compared with ARz (r = 0.91 vs 0.24). Eighteen patients underwent surgery. Surgical procedures included at least 2 components in 17 (aortic, mitral, tricuspid, aortic root, and arch procedures) and isolated mitral valve procedures in 1 patient. Time-related transition to surgery showed a prominent early phase to 1 year post presentation, followed by a slowly increasing late phase. CSA/Ht had a more linear correlation versus ARz during periods of rapid somatic growth in surgical patients. Surgical repair occurred at CSA/Ht between 5 and 7 cm2/m. ConclusionsCSA/Ht tracked ARd well over time. CSA/Ht between 5 and 7 cm2/m might be a promising metric for surgical triage in pMFS patients. CSA/Ht surgical threshold values in pMFS patients occurred at lower than current accepted “surgical” threshold values for CSA/Ht in adult Marfan syndrome patients.

A time-varying GARCH mixed-effects model for isolating high- and low- frequency volatility and co-volatility

This article studies long-term, short-term volatility and co-volatility in stock markets by introducing modelling strategies to the multivariate data analysis that deal with serially correlated innovations and cross-section dependence. In particular, it presents an innovative mixed-effects model through a GARCH process, allowing for heterogeneity effects and time-series dynamics. We propose a non-parametric regression model of the penalized low-rank smoothing spline to present time trends into the variance and covariance equations. The strategy provides flexible modelling of the low-frequency volatility and co-volatility in equity markets. The decomposed low-frequency matrix was modelled using the modified Cholesky factorization. The Hamiltonian Monte Carlo technique is implemented as a Bayesian computing process for estimating parameters and latent factors. The advantage of our modelling strategy in empirical studies is highlighted by examining the effect of latent financial factors on a panel across 10 equities over 110 weekly series. The model can differentiate non-parametrically dynamic patterns of high and low frequencies of variance–covariance structural equations and incorporate economic features to predict variabilities in stock markets regarding time-series evidence.

A generalized correlated Cp criterion for derivative estimation with dependent errors

In practice, it is common that errors are correlated for the nonparametric regression model. Although many methods have been developed for addressing correlated errors for tuning parameter selection to recover the mean response function, few studies have been proposed to select tuning parameters for derivative estimation. In this paper, a generalized correlated Cp (GCCp) criterion is proposed to choose a tuning parameter for derivative estimation in the presence of correlated errors. It can be applied for any nonparametric estimation linear in responses, including kernel regression, local regression, smoothing spline, etc. The GCCp criterion is justified both theoretically and empirically via simulation studies. Finally, an air quality index data example in Changsha city is provided to illustrate the application of the proposed criterion.

Retrieval of Crop Variables from Proximal Multispectral UAV Image Data Using PROSAIL in Maize Canopy.

Mapping crop variables at different growth stages is crucial to inform farmers and plant breeders about the crop status. For mapping purposes, inversion of canopy radiative transfer models (RTMs) is a viable alternative to parametric and non-parametric regression models, which often lack transferability in time and space. Due to the physical nature of RTMs, inversion outputs can be delivered in sound physical units that reflect the underlying processes in the canopy. In this study, we explored the capabilities of the coupled leaf–canopy RTM PROSAIL applied to high-spatial-resolution (0.015 m) multispectral unmanned aerial vehicle (UAV) data to retrieve the leaf chlorophyll content (LCC), leaf area index (LAI) and canopy chlorophyll content (CCC) of sweet and silage maize throughout one growing season. Two different retrieval methods were tested: (i) applying the RTM inversion scheme to mean reflectance data derived from single breeding plots (mean reflectance approach) and (ii) applying the same inversion scheme to an orthomosaic to separately retrieve the target variables for each pixel of the breeding plots (pixel-based approach). For LCC retrieval, soil and shaded pixels were removed by applying simple vegetation index thresholding. Retrieval of LCC from UAV data yielded promising results compared to ground measurements (sweet maize RMSE = 4.92 μg/cm2, silage maize RMSE = 3.74 μg/cm2) when using the mean reflectance approach. LAI retrieval was more challenging due to the blending of sunlit and shaded pixels present in the UAV data, but worked well at the early developmental stages (sweet maize RMSE = 0.70m2/m2, silage RMSE = 0.61m2/m2 across all dates). CCC retrieval significantly benefited from the pixel-based approach compared to the mean reflectance approach (RMSEs decreased from 45.6 to 33.1 μg/m2). We argue that high-resolution UAV imagery is well suited for LCC retrieval, as shadows and background soil can be precisely removed, leaving only green plant pixels for the analysis. As for retrieving LAI, it proved to be challenging for two distinct varieties of maize that were characterized by contrasting canopy geometry.