Semi-varying Coefficient Models Research Articles

Variable selection for semivarying coefficient models via local averaging

AbstractThis study aims to provide novel insights into variable selection in the semivarying coefficient model. We focus on the problem of variable selection and screening for the constant coefficient part. A common approach in the existing literature is to infer the constant coefficients by transforming the problem into a linear model scenario, utilizing a fine estimator of the varying coefficients. In this paper, we propose an approximation method for the varying coefficient functions using local averaging, which is characterized by its simplicity, rough and computational efficiency. Additionally, we introduce an adaptive lasso estimator and a forward regression algorithm specifically designed for semivarying coefficient models. Theoretical and experimental results highlight the effectiveness of the local averaging method in extending variable selection techniques from the linear model to the semivarying coefficient model. Our proposed approaches demonstrate a significant improvement in inference speed compared with baseline methods, with little loss of asymptotic efficiency.

Estimation of semi-varying coefficient models for longitudinal data with irregular error structure

Semiparametric models are often considered for modeling longitudinal data for a good balance between flexibility and parsimony. In this paper, we focus on the estimation for a longitudinal semi-varying coefficient model which is of irregular errors. A semiparametric profile least-squares method is developed to estimate parameters in the mean function and error structure simultaneously. Then, a two-stage local linear estimator is investigated for the nonparametric part. Further, we establish the asymptotic properties of the resulting estimators under some mild conditions. The practical problems of implementation are also addressed. Finally, three numerical experiments are conducted to verify the finite sample performance of the proposed methods, and an application to the CD4 cell data is provided for illustration.

Adaptive-weighted estimation of semi-varying coefficient models with heteroscedastic errors

An adaptive-weighted estimation procedure for parametric and nonparametric coefficients in semi-varying coefficient models with heteroscedastic errors is considered in this paper. Firstly, we present a consistent estimator of the variance function of the error term. In order to take the heteroscedasticity into consideration, we consider the weighted local linear smoothing technique. Asymptotic properties of the proposed estimators are established. Our theoretical results demonstrate that the adaptive-weighted estimator is more efficient than the unweighted profile least-squares estimators. The simulation results show that our adaptive-weighted estimators are more efficient, compared to profile least-squares estimators and re-weighted estimators under the finite sample size. Finally, our estimation procedure is applied to a real-world data.

The Real-time Effect of Public Health Interventions on the COVID-19 Epidemic in Hubei Province

The Corona Virus Disease 2019 (COVID-19) emerged in Wuhan, China in December 2019. In order to control the epidemic, the Chinese government adopted several public health measures. To study the influence of these measures on the transmissibility of COVID-19 in the city of Wuhan and other cities in the Hubei province, China, we establish generalized semi-varying coefficient models for the number of new diagnosed cases and estimate the varying coefficient for the covariates by the spline method. Since the pandemic was most severe in Wuhan, we fitted separate models for Wuhan and the remaining 16 cities in Hubei. Estimators for the incubation periods, the real-time transmission rates, and the real-time reproduction numbers were obtained. The results demonstrate that the changes in the real-time transmission rate in Wuhan and other cities in Hubei are almost simultaneous. Futher, public health interventions such as restriction of traffic, adjustment of the diagnosed standard, deployment of medical resources, and improvement of nucleic acid testing capacity, had positive effects on reducing the transmission of COVID-19.

Semi-Varying Coefficient Models Explore the Housing Price Problem for AMES City of Iowa State in American

Semi-Varying Coefficient Models Explore the Housing Price Problem for AMES City of Iowa State in American

Fast inference for semi-varying coefficient models via local averaging

The semi-varying coefficient models are widely used in the application of finance, economics, medical science and many other areas. In general, the functional coefficients are estimated by local smoothing methods, e.g. local linear estimator. So the computation cost is severe because one should point-wisely estimate the value of a coefficient function. In this paper, we give an insight into the trade-off between statistical efficiency and computation simplicity and proposes a fast inference procedure, local average estimator. The proposed method is easy to implement and avoid repeat estimation since it approximates the coefficient functions with piecewise constants. Though the local average estimator is not asymptotically optimal, it is still efficient enough for further inference. Thus, three tests are derived to check whether a coefficient is constant. The experimental evidence shows that when there is limited room for improving the asymptotic efficiency, a proper trade-off between statistical efficiency and computation simplicity may improve the finite-sample performance.

Testing constancy in varying coefficient models

This article proposes a coefficients constancy test in semi-varying coefficient models that only needs to estimate the restricted coefficients under the null hypothesis. The test statistic resembles the union-intersection test after ordering the data according to the varying coefficients’ explanatory variable. This statistic depends on a trimming parameter that can be chosen by a data-driven calibration method we propose. A bootstrap test is justified under fairly general regularity conditions. Under more restrictive assumptions, the critical values can be tabulated, and trimming is unnecessary. The finite sample performance is studied by means of Monte Carlo experiments, and a real data application for modeling education returns.

A Tree-Based Semi-Varying Coefficient Model for the COM-Poisson Distribution

We propose a tree-based semi-varying coefficient model for the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution which is a two-parameter generalization of the Poisson distribution and is flexible enough to capture both under-dispersion and over-dispersion in count data. The advantage of tree-based methods is their scalability to high-dimensional data. We develop CMPMOB, an estimation procedure for a semi-varying coefficient model, using model-based recursive partitioning (MOB). The proposed framework is broader than the existing MOB framework as it allows node-invariant effects to be included in the model. To simplify the computational burden of the exhaustive search employed in the original MOB algorithm, a new split point estimation procedure is proposed by borrowing tools from change point estimation methodology. The proposed method uses only the estimated score functions without fitting models for each split point and, therefore, is computationally simpler. Since the tree-based methods only provide a piece-wise constant approximation to the underlying smooth function, we further propose the CMPBoost semi-varying coefficient model which uses the gradient boosting procedure for estimation. The usefulness of the proposed methods are illustrated using simulation studies and a real example from a bike sharing system in Washington, DC. Supplementary files for this article are available online.

Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection

Modal regression is a good alternative of the mean regression, because of its merits of both robustness and high inference efficiency. This paper is concerned with modal regression based statistical inference for semivarying coefficient models with longitudinal data, which include modal regression generalized estimating equations, modal regression empirical likelihood inference procedure for the parametric component and smooth- threshold modal regression generalized estimating equations for variable selection. These methods can incorporate the correlation structure of the longitudinal data and inherit the robustness and efficiency superiorities of the modal regression by choosing an appropriate data adaptive tuning parameter. Under mild conditions, the large sample theoretical properties are established. Simulation studies and real data analysis are also included to illustrate the finite sample performance.

Robust conditional nonparametric independence screening for ultrahigh-dimensional data

This article novelly proposes a robust model-free screening procedure, which performs well for a variety of semivarying coefficient models. Under technical conditions, we show that it possesses the ranking consistency property and the sure screening property. Comprehensive simulation studies are conducted to demonstrate that it exhibits more competitive performance than existing screening methods.

Estimation and inference for generalized semi-varying coefficient models

ABSTRACTThis paper is concerned with the estimation and inference in generalized semi-varying coefficient models. An orthogonal projection local quasi-likelihood estimation is investigated, which can easily be used to estimate the model parametric and nonparametric parts. Then an empirical likelihood logarithmic approach to construct the confidence regions/intervals of the nonparametric parts is developed. Under some mild conditions, the asymptotic properties of the resulting estimators are studied explicitly, respectively. Some simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by a real data set.

The consistency of model selection for dynamic Semi-varying coefficient models with autocorrelated errors

ABSTRACTThe consistency of model selection criterion BIC has been well and widely studied for many nonlinear regression models. However, few of them had considered models with lag variables as regressors and auto-correlated errors in time series settings, which is common in both linear and nonlinear time series modeling. This paper studies a dynamic semi-varying coefficient model with ARMA errors, using an approach based on spectrum analysis of time series. The consistency property of the proposed model selection criteria is established and an implementation procedure of model selection is proposed for practitioners. Simulation studies have also been conducted to numerically show the consistency property.

Heterogeneous treatment effects of safe water on infectious disease: Do meteorological factors matter?

Mortality from waterborne infectious diseases remains a serious issue globally. Investigating the efficient laying plan of waterworks to mitigate the risk factors for such diseases has been an important research avenue for industrializing countries. While a growing body of the literature has revealed the mitigating effects of water-purification facilities on diseases, the heterogeneous treatment effects of clean water have been understudied. The present study thus focuses on the treatment effect heterogeneity of piped water with respect to the external meteorological environment of cities in industrializing Japan. To estimate the varying effects, we implement fixed-effects semivarying coefficient models to deal with the unobservable confounding factors, using a nationwide city-level panel dataset between 1922 and 1940. We find evidence that the magnitude of safe water on the reduction in the typhoid death rate is larger in cities with a higher temperature, which is consistent with recent epidemiological evidence. These findings underscore the importance of the variations in the external meteorological conditions of the municipalities that install water-purification facilities in developing countries.

Semivarying coefficient least-squares support vector regression for analyzing high-dimensional gene-environmental data

ABSTRACTIn the context of genetics and genomic medicine, gene-environment (G×E) interactions have a great impact on the risk of human diseases. Some existing methods for identifying G×E interactions are considered to be limited, since they analyze one or a few number of G factors at a time, assume linear effects of E factors, and use inefficient selection methods. In this paper, we propose a new method to identify significant main effects and G×E interactions. This is based on a semivarying coefficient least-squares support vector regression (LS-SVR) technique, which is devised by utilizing flexible semiparametric LS-SVR approach for censored survival data. This semivarying coefficient model is used to deal with the nonlinear effects of E factors. We also derive a generalized cross validation (GCV) function for determining the optimal values of hyperparameters of the proposed method. This GCV function is also used to identify significant main effects and G×E interactions. The proposed method is evaluated through numerical studies.

Variable selection and structure identification for varying coefficient Cox models

We consider varying coefficient Cox models with high-dimensional covariates. We apply the group Lasso to these models and propose a variable selection procedure. Our procedure can cope with simultaneous variable selection and structure identification for high-dimensional varying coefficient models to find true semi-varying coefficient models from them. We also derive an oracle inequality and closely examine restrictive eigenvalue conditions. We focus on Cox models with time-varying coefficients. The theoretical results on variable selection can be extended easily to some other important models which we only mention briefly since they can be treated in the same way. The models considered here are the most popular among structured nonparametric regression models. The results of numerical studies are also reported.

Variable selection for spatial semivarying coefficient models

Spatial semiparametric varying coefficient models are a useful extension of spatial linear model. Nevertheless, how to conduct variable selection for it has not been well investigated. In this paper, by basis spline approximation together with a general M-type loss function to treat mean, median, quantile and robust mean regressions in one setting, we propose a novel partially adaptive group $$L_{r} (r\ge 1)$$ penalized M-type estimator, which can select variables and estimate coefficients simultaneously. Under mild conditions, the selection consistency and oracle property in estimation are established. The new method has several distinctive features: (1) it achieves robustness against outliers and heavy-tail distributions; (2) it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles; (3) it can keep balance between efficiency and robustness. Simulation studies and real data analysis are included to illustrate our approach.

Robust bootstrap estimates in heteroscedastic semi-varying coefficient models and applications in analyzing Australia CPI data

ABSTRACTThis article deals with the estimation of the parametric component, which is of primary interest, in the heteroscedastic semi-varying coefficient models. Based on the bootstrap technique, we present a procedure for estimating the parameters, which can provide a reliable approximation to the asymptotic distribution of the profile least-square (PLS) estimator. Furthermore, a bootstrap-type estimator of covariance matrix is developed, which is proved to be a consistent estimator of the covariance matrix. Moreover, some simulation experiments are conducted to evaluate the finite sample performance for the proposed methodology. Finally, the Australia CPI dataset is analyzed to demonstrate the application of the methods.

Empirical likelihood for semi-varying coefficient models for panel data with fixed effects

The empirical likelihood inference for semi-varying coefficient models for panel data with fixed effects is investigated in this paper. We propose an empirical log-likelihood ratio function for the regression parameters in the model under α-mixing condition. The empirical log-likelihood ratio is proven to be asymptotically chi-squared. We also obtain the maximum empirical likelihood estimator of the parameters of interest, and prove that it is the asymptotically normal under some suitable conditions. A simulation study and a real data application are undertaken to assess the finite sample performance of our proposed method.

Model selection and structure specification in ultra-high dimensional generalised semi-varying coefficient models

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO penalty (or the local linear approximation of the group SCAD penalty) with the help of the preliminary estimation of the functional coefficients, we introduce a novel penalised weighted least squares procedure to select the significant covariates and identify the constant coefficients among the coefficients of the selected covariates, which could thus specify the semiparametric modelling structure. The developed model selection and structure specification approach not only inherits many nice statistical properties from the local maximum likelihood estimation and nonconcave penalised likelihood method, but also computationally attractive thanks to the computational algorithm that is proposed to implement our method. Under some mild conditions, we establish the asymptotic properties for the proposed model selection and estimation procedure such as the sparsity and oracle property. We also conduct simulation studies to examine the finite sample performance of the proposed method, and finally apply the method to analyse a real data set, which leads to some interesting findings.

Estimation of semi-varying coefficient models with nonstationary regressors

ABSTRACTWe study a semivarying coefficient model where the regressors are generated by the multivariate unit root I(1) processes. The influence of the explanatory vectors on the response variable satisfies the semiparametric partially linear structure with the nonlinear component being functional coefficients. A semiparametric estimation methodology with the first-stage local polynomial smoothing is applied to estimate both the constant coefficients in the linear component and the functional coefficients in the nonlinear component. The asymptotic distribution theory for the proposed semiparametric estimators is established under some mild conditions, from which both the parametric and nonparametric estimators are shown to enjoy the well-known super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the developed methodology and results.