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Variable selection of the quantile varying coefficient regression models
Riquan Zhang,Weihua Zhao,Yazhao Lv,Jicai Liu 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.3
As a useful supplement to mean regression, quantile regression is a completely distribution-free approach and is more robust to heavy-tailed random errors. In this paper, a variable selection procedure for quantile varying coefficient models is proposed by combining local polynomial smoothing with adaptive group LASSO. With an appropriate selection of tuning parameters by the BIC criterion, the theoretical properties of the new procedure,including consistency in variable selection and the oracle property in estimation, are established. The finite sample performance of the newly proposed method is investigated through simulation studies and the analysis of Boston house price data. Numerical studies confirm that the newly proposed procedure (QKLASSO) has both robustness and efficiency for varying coefficient models irrespective of error distribution, which is a good alternative and necessary supplement to the KLASSO method.
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TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
Zhensheng Huang,Riquan Zhang 대한수학회 2010 대한수학회지 Vol.47 No.2
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the Â2-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
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Local estimation for longitudinal semiparametric varying-coefficient partially linear model
Yanghui Liu,Riquan Zhang,Hongmei Lin 한국통계학회 2017 Journal of the Korean Statistical Society Vol.46 No.2
In this paper, estimation for the semiparametric varying coefficient partially linear model with longitudinal data is investigated. We propose an intuitive procedure to estimate the regression function and the covariance structure simultaneously based on the modified Cholesky decomposition and profile least square technique. The asymptotic normality of the resulting estimators is further derived. Moreover, we develop a variable selection procedure to select significant parameter components for the model within the framework of profile least square estimate. A simulation study is conducted to illustrate the finitesample performance of the estimation and variable selection procedures. Finally, the proposed method is applied to analyze a set of chronic kidney disease (CKD) progression data in a study of the relationship between glomerular filtration rate (GFR) and the risk factors among CKD patients.
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TESTS FOR VARYING-COEFFICIENT PARTS ON VARYING-COEFFICIENT SINGLE-INDEX MODEL
Huang, Zhensheng,Zhang, Riquan Korean Mathematical Society 2010 대한수학회지 Vol.47 No.2
To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.
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Robust estimation for a general functional single index model via quantile regression
Zhu Hanbing,Zhang Riquan,Liu Yanghui,Ding Hui 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.4
This paper studies the estimation of a general functional single index model, in which the conditional distribution of the response depends on the functional predictor via a functional single index structure. We find that the slope function can be estimated consistently by the estimation obtained by fitting a misspecified functional linear quantile regression model under some mild conditions. We first obtain a consistent estimator of the slope function using functional linear quantile regression based on functional principal component analysis, and then employ a local linear regression technique to estimate the conditional quantile function and establish the asymptotic normality of the resulting estimator for it. The finite sample performance of the proposed estimation method is studied in Monte Carlo simulations, and is illustrated by an application to a real dataset.
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Zou Yuye,Fan Guoliang,Zhang Riquan 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.1
In this paper, we focus on the empirical likelihood inference for partially linear single-index errors-in-variables (EV) models when the data are right censored and the censoring indicator is missing at random (MAR). Two bias-corrected empirical log-likelihood ratio (BCELR) functions for the parameters by using regressing calibration and imputation methods are introduced. The limiting distributions of the BCELRs are shown to have a mixture of central chi-squared distribution. Based on this, the confdence regions of the parameters can be constructed by using bootstrap approximation. Furthermore, as there would be some spurious covariates in the linear and nonlinear parts, a penalized empirical likelihood (PEL) approach is proposed with the help of smoothly clipped absolute deviation penalty. Two proposed PEL estimators are shown to possess the oracle property. A simulation study and a real data analysis are conducted to evaluate the fnite sample performance of the proposed methods.
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Empirical likelihood for the class of single index hazard regression models
Jianbo Li,Minglong Guo,Changxin Du,Riquan Zhang,Heng Lian 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.4
Based on the B spline approximation technique and right censored data, we consider the empirical likelihood inference for the index parameters and its partial components in a class of single index hazard regression models. Under some regular conditions, we show that our proposed empirical likelihood ratio statistics follow the standard χ2 distribution. Some numerical studies are given to illustrate our proposed methodology.
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