Robust estimation and variable selection for varying-coefficient partially nonlinear models based on modal regression

다국어 초록 (Multilingual Abstract)

In this paper, we propose a robust two-stage estimation and variable selection procedure for varying-coefficient partially nonlinear model based on modal regression.
In the first stage, each coefficient function is approximated by B-spline basis functions and then QR decomposition is employed to remove the nonparametric component from the original model.
For the simple parametric model, an estimation and variable selection procedure for parameter is proposed based on modal regression.
In the second stage, similar procedure for coefficient function is developed.
The proposed procedure is not only flexible and easy to implement, but also is robust and efficient.
Under some mild conditions, certain asymptotic properties of the resulting estimators are established.
Moreover, the bandwidth selection and estimation algorithm for the proposed method is discussed.
Furthermore, we conduct some simulations and a real example to evaluate the performances of the proposed estimation and variable selection procedure in finite samples.

참고문헌 (Reference)

1 Zhou, Z. Y., "Varying coefcient partially nonlinear models with nonstationary regressors" 194 : 47-64, 2018

2 Fan, J. Q., "Variable selection via nonconcave penalized likelihood and its oracle properties" 9 : 1348-1360, 2001

3 Xia, Y. F., "Variable selection for semiparametric varying coefcient partially linear model based on modal regression with missing data" 48 : 5121-5137, 2019

4 Wang, X. L., "Statistical inferences for varying coefcient partially non linear model with missing covariates" 50 : 2599-2618, 2021

5 Schumaker, L. L., "Spline Function" Wiley 1981

6 Yang, J., "Smooth-threshold estimating equations for varying coefcient partially nonlinear models based on orthogonality-projection method" 302 : 24-37, 2016

7 Yang, J., "Robust variable selection of varying coeffcient partially nonlinear model based on quantile regression" 12 : 397-413, 2019

8 Lv, Z. K., "Robust variable selection for nonlinear models with diverging number for parameters" 91 : 90-97, 2014

9 Jiang, Y. L., "Robust estimation for the varying coefcient partially nonlinear models" 326 : 31-43, 2017

10 Zhang, R. Q., "Robust estimation and variable selection for semiparametric partially linear varying coefcient model based on modal regression" 25 : 523-544, 2013

11 Zhao, W. H., "Robust and efcient variable selection for semiparametric partially linear varying coefcient model based on modal regression" 66 : 165-191, 2014

12 Jing Yang ; Fang Lu ; Hu Yang, "Quantile regression for robust inference on varying coefficient partially nonlinear models" 한국통계학회 47 (47): 172-184, 2018

13 Huang, J. T., "QR decomposition based orthogonality estimation for partially linear models with longitudinal data" 321 : 406-415, 2017

14 Wang, K. N., "Modal regression statistical inference for longitudinal data semivarying coefcient models : Generalized estimating equations, empirical likelihood and variable selection" 133 : 257-276, 2019

15 Yao, W., "Local modal regression" 24 : 647-663, 2012

16 Shuang Dai ; Zhensheng Huang, "Estimation for varying coefficient partially nonlinear models with distorted measurement errors" 한국통계학회 48 (48): 117-133, 2019

17 Li, T. Z., "Estimation and inference for varying coefcient partially nonlinear models" 143 : 2023-2037, 2013

18 Zhou, X. S., "Empirical likelihood inferences for varying coefcient partially nonlinear models" 44 : 474-492, 2017

19 Xiao, Y. T., "Bias-corrected estimations in varying-coefcient partially nonlinear models with measurement error in the nonparametric part" 45 : 586-603, 2018

20 Wu, P., "An orthogonality-based estimation of moments for linear mixed models" 37 : 253-263, 2010

21 Tang, X. R., "Adjusted empirical likelihood inferences for varying coefcient partially non linear models with endogenous covariates" 2020

22 Li, J., "A nonparametric statistical approach to clustering via mode identifcation" 8 : 1687-1723, 2007

23 Yao, W., "A new regression model : modal linear regression" 41 : 656-671, 2014

24 Peixin Zhao ; Yiping Yang, "A new orthogonality-based estimation for varying-coefficient partially linear models" 한국통계학회 48 (48): 29-39, 2019