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Data are heterogeneous when recorded in different time regimes or taken from multiple sources to some degree. Varying-coefficient models or mixture models are suitable for solving this type of problem. On one hand, existing models are quite complicated and computationally cumbersome especially for large-scale data. On the other hand, common effects among different data sources are unknown. Additionally, some existing models are unable to search the non linear relationship between response and covariates. To address these challenges, we aim at estimating common effects about non parametric regression when data are heterogeneous. Our proposed estimation method is based on basis function expansion. Adaptive basis series and fixed basis series are considered, respectively. We exploit maximin aggregation technique to get a simple non linear model, also the common effects, from all possible grouped data. The mean squared error and asymptotic distribution of the estimator are investigated. Simulation studies and real-data analysis are conducted to verify the efficiency of the estimation procedure. Comparing with ordinary least square estimator and averaging ordinary least square estimator, our proposed estimator can reduce the complexity of data sources and is more robust. [ABSTRACT FROM AUTHOR]

Three-dimensional printing technology is a rapid prototyping technology that has been widely used in manufacturing. However, the printing parameters in the 3D printing process have an important impact on the printing effect, so these parameters need to be optimized to obtain the best printing effect. In order to further understand the impact of 3D printing parameters on the printing effect, make theoretical explanations from the dimensions of mathematical models, and clarify the rationality of certain important parameters in previous experience, the purpose of this study is to predict the impact of 3D printing parameters on the printing effect by using machine learning methods. Specifically, we used four machine learning algorithms: SVR (support vector regression): A regression method that uses the principle of structural risk minimization to find a hyperplane in a high-dimensional space that best fits the data, with the goal of minimizing the generalization error bound. Random forest: An ensemble learning method that constructs a multitude of decision trees and outputs the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. GBDT (gradient boosting decision tree): An iterative ensemble technique that combines multiple weak prediction models (decision trees) into a strong one by sequentially minimizing the loss function. Each subsequent tree is built to correct the errors of the previous tree. XGB (extreme gradient boosting): An optimized and efficient implementation of gradient boosting that incorporates various techniques to improve the performance of gradient boosting frameworks, such as regularization and sparsity-aware splitting algorithms. The influence of the print parameters on the results under the feature importance and SHAP (Shapley additive explanation) values is compared to determine which parameters have the greatest impact on the print effect. We also used feature importance and SHAP values to compare the importance impact of print parameters on results. In the experiment, we used a dataset with multiple parameters and divided it into a training set and a test set. Through Bayesian optimization and grid search, we determined the best hyperparameters for each algorithm and used the best model to make predictions for the test set. We compare the predictive performance of each model and confirm that the extrusion expansion ratio, elastic modulus, and elongation at break have the greatest influence on the printing effect, which is consistent with the experience. In future, we will continue to delve into methods for optimizing 3D printing parameters and explore how interpretive machine learning can be applied to the 3D printing process to achieve more efficient and reliable printing results. [ABSTRACT FROM AUTHOR]

This article considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable quantile regression approach is employed for parameter estimation. The rank score tests are developed for hypotheses on the coefficients, including the hypotheses on the non-varying coefficients and the constancy of the varying coefficients. The asymptotic properties of the proposed estimators and test statistics are both established. Monte Carlo simulations are conducted to study the finite sample performance of the proposed method. Analysis of a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

Modern spatial temporal data are often collected from sensor networks. Missing data problems are common to this kind of data. Making accurate imputation is important for many applications. In the unsupervised setting, one technique is to minimize the rank of a tensor or matrix. If we add related covariates, can we get more accurate imputation results? To address this, we transform the original sensor×time measurements to high order tensors by adding additional temporal dimensions and then integrate tensor regression with tensor completion using nuclear norm penalty. One advantage is we can simultaneously estimate parameters and impute missing values due to clear spatial consistency for near-sited spatial-temporal data. The proposed method doesn't assume missing mechanism of the response. Theoretical properties of the proposed estimator are investigated. Simulation studies and real data analysis are conducted to verify the efficiency of the estimation procedure. [ABSTRACT FROM AUTHOR]

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles. [ABSTRACT FROM AUTHOR]

In spatio‐temporal epidemiological analysis, it is of critical importance to identify the significant covariates and estimate the associated time‐varying effects on the health outcome. Due to the heterogeneity of spatio‐temporal data, the subsets of important covariates may vary across space and the temporal trends of covariate effects could be locally different. However, many spatial models neglected the potential local variation patterns, leading to inappropriate inference. Thus, this article proposes a flexible Bayesian hierarchical model to simultaneously identify spatial clusters of regression coefficients with common temporal trends, select significant covariates for each spatial group by introducing binary entry parameters and estimate spatio‐temporally varying disease risks. A multistage strategy is employed to reduce the confounding bias caused by spatially structured random components. A simulation study demonstrates the outperformance of the proposed method, compared with several alternatives based on different assessment criteria. The methodology is motivated by two important case studies. The first concerns the low birth weight incidence data in 159 counties of Georgia, USA, for the years 2007 to 2018 and investigates the time‐varying effects of potential contributing covariates in different cluster regions. The second concerns the circulatory disease risks across 323 local authorities in England over 10 years and explores the underlying spatial clusters and associated important risk factors. [ABSTRACT FROM AUTHOR]

Practitioners of current data analysis are regularly confronted with the situation where the heavy‐tailed skewed response is related to both multiple functional predictors and high‐dimensional scalar covariates. We propose a new class of partially functional penalized convolution‐type smoothed quantile regression to characterize the conditional quantile level between a scalar response and predictors of both functional and scalar types. The new approach overcomes the lack of smoothness and severe convexity of the standard quantile empirical loss, considerably improving the computing efficiency of partially functional quantile regression. We investigate a folded concave penalized estimator for simultaneous variable selection and estimation by the modified local adaptive majorize‐minimization (LAMM) algorithm. The functional predictors can be dense or sparse and are approximated by the principal component basis. Under mild conditions, the consistency and oracle properties of the resulting estimators are established. Simulation studies demonstrate a competitive performance against the partially functional standard penalized quantile regression. A real application using Alzheimer's Disease Neuroimaging Initiative data is utilized to illustrate the practicality of the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes two new weighted quantile regression estimators for static panel data model with time-invariant regressors. The two new estimators can improve the estimation of the coefficients with time-invariant regressors, which are computationally convenient and simple to implement. Also, the paper shows consistency and asymptotic normality of the two proposed estimator for sequential and simultaneous N, T asymptotics. Monte Carlo simulation in various parameters sets proves the validity of the proposed approach. It has an empirical application to study the effects of the influence factors of China's exports using the trade gravity model. [ABSTRACT FROM AUTHOR]

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures. [ABSTRACT FROM AUTHOR]

An innovated model‐free interaction screening procedure called the MCVIS is proposed for high dimensional data analysis. Specifically, we adopt the introduced MCV index for quantifying the importance of an interaction effect among predictors. Our proposed method is fully nonparametric and is capable of successfully selecting interactions even if the signal of parental main effects is weak. The MCVIS procedure has many distinctive features: (i) it can work with discrete, categorical and continuous covariates; (ii) it can deal with both categorical and continuous response, even handle the missing response; (iii) it is robust for heavy‐tailed distributions, thus well accommodates heterogeneity typically caused by high dimensionality; (iv) it enjoys the sure screening and ranking consistency properties, therefore achieves dimension reduction without information loss. In another respect, computational feasibility is a top concern in high dimensional data analysis, by transforming our MCV into several variants, the MCVIS procedure is simple and fast to implement. Extensive numerical experiments and comparisons confirm the effectiveness and wide applicability of our MCVIS procedure. We further illustrate the proposed methodology by empirical study of two real datasets. Supplementary materials are available online. [ABSTRACT FROM AUTHOR]

Time dynamic varying coefficient models play an important role in applications of biology, medicine, environment, finance, etc. Traditional methods, such as kernel smoothing and spline smoothing, are popular. But explicit expressions are unavailable using these methods, and the convergence rate of coefficient function estimators is slow. To address these problems, we expand the varying component with appropriate basis functions. And then we solve a sparse regression problem via a sequential thresholded least-squares estimator. The "parameterization" leads to explicit expressions and fast computation speed. Convergence of the sequential thresholded least squares algorithm is guaranteed. The asymptotic distribution of the coefficient function estimator is derived under certain assumptions. Our simulation shows the proposed method has higher precision and computing speed. Finally, our proposed method is applied to the study of PM 2.5 concentration in Beijing. We analyze the relationship between PM 2.5 and other impact factors. [ABSTRACT FROM AUTHOR]

This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for approximating varying coefficients, including B-spline and local polynomial approximation. A fixed-effects quantile regression (FEQR) estimator is typically biased in the presence of the spatial lag variable. The wild bootstrap method is employed to attenuate the estimation bias. Simulations are conducted to study the performance of the proposed method and show that the proposed methods are stable and efficient. Further, the estimators based on the B-spline method perform much better than those of the local polynomial approximation method, especially for location-varying coefficients. Real data about economic development in China are also analyzed to illustrate application of the proposed procedure. [ABSTRACT FROM AUTHOR]

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure. [ABSTRACT FROM AUTHOR]

Understanding how health care costs vary across different demographics and health conditions is essential to developing policies for health care cost reduction. It may not be optimal to apply the conventional mean regression due to its sensitivity to the high level of skewness and spatio‐temporal heterogeneity presented in the cost data. To find an alternative method for spatio‐temporal analysis with robustness and high estimation efficiency, we combine information across multiple quantiles and propose a Bayesian spatio‐temporal weighted composite quantile regression (ST‐WCQR) model. An easy‐to‐implement Gibbs sampling algorithm is provided based on the asymmetric Laplace mixture representation of the error term. Extensive simulation studies show that ST‐WCQR outperforms existing methods for skewed error distributions. We apply ST‐WCQR to investigate how patients' characteristics affected the inpatient hospital costs for alcohol‐related disorders and identify areas that could be targeted for cost reduction in New York State from 2015 to 2017. [ABSTRACT FROM AUTHOR]

The transmission of coronavirus disease‐2019 (COVID‐19) epidemic is a global emergency, which is worsened by the genetic mutations of SARS‐CoV‐2. However, till date, few statistical studies have researched the COVID‐19 spread patterns in terms of the variant cases. Hence, this paper aims to explore the associated risk factors of Delta variant, the most contagious strain of COVID‐19. The study collected the state‐level COVID‐19 Delta variant cases in the United States during a 12‐week period and included potential environmental, socioeconomic, and public prevention factors as independent variables. Instead of regarding the covariate effects as constant, this paper proposes a flexible Bayesian hierarchical model with spatio‐temporally varying coefficients to account for data heterogeneity. The method enables us to cluster the states into distinctive groups based on the temporal trends of the coefficients and simultaneously identify significant risk factors for each cluster. The findings contribute novel insight into the dynamics of covariate effects on the COVID‐19 Delta variant over space and time, which could help the government develop targeted prevention measures for vulnerable regions based on the selected risk factors. [ABSTRACT FROM AUTHOR]

This paper studies variable selection for the data set, which has heavy-tailed distribution and high correlations within blocks of covariates. Motivated by econometric and financial studies, we consider using quantile regression to model the heavy-tailed distribution data. Considering the case where the covariates are high dimensional and there are high correlations within blocks, we use the latent factor model to reduce the correlations between the covariates and use the conquer to obtain the estimators of quantile regression coefficients, and we propose a consistency strategy named factor-augmented regularized variable selection for quantile regression (Farvsqr). By principal component analysis, we can obtain the latent factors and idiosyncratic components; then, we use both as predictors instead of the covariates with high correlations. Farvsqr transforms the problem from variable selection with highly correlated covariates to that with weakly correlated ones for quantile regression. Variable selection consistency is obtained under mild conditions. Simulation study and real data application demonstrate that our method is better than the common regularized M-estimation LASSO. [ABSTRACT FROM AUTHOR]