Penalized Weighted Composite Quantile Regression Method For Nonlinear Panel Models

Nonlinear relationship is central to applied studies,since answering real-world research questions using data typically requires complex nonlinear models to adequately represent the system under study.However,despite some recent progress,the literature is still short of answers for many models commonly used in the empirical work.More broadly,to date no approach is yet available to specify and estimate general data relationships in longitudinal settings especially when the error is a non-Gaussian distribution.Since compared to the mean regression model,the stochastic relationship between random variables,by using quantiles,can be better portrayed and with much more accuracy.However,a straightforward use of quantile regression leads to biased estimators of parameters in some complicated models.To further improve upon the usual quantile regression,Jiang et al.(2012)suggested a weighted composite quantile regression estimation method and let the data decide the weights to improve efficiency,while keeping robustness from the quantile regression.?In addition,various techniques have been developed for simultaneous variable selection and coefficient estimation,based on the penalized likelihood or least squares principles.Taking this issue into account,and motivated by the studies,in this paper,we address the issue of nonlinear panel models using a new weighted composite quantile regression estimator with variable selection.We establish asymptotic properties of the proposed estimators.The proposed method avoids estimating the unknown error density function involved in the asymptotic covariance matrix of the estimators.The simulations and real data analysis suggest that the proposed procedure is more efficient and robust.Hence,this paper provides a positive result of the weighted composite quantile regression modeling,and extends the application literature of the proposed method.?The main contents are organized as follows:In chapter 1,we first give a brief overview of the research background.Then,with common research content,we introduce nonlinear panel models,weighted composite quantile regression and variable selection.Finally,we describe the the main content and innovation of paper.In chapter 2,we propose the weighted composite quantile regression for nonlinear panel models with a penalized fixed effects.Then,under regularity conditions,we establish asymptotic properties of the proposed estimators,and the choice of weights is also given in this chapter.Furthermore,proofs of the theorem are given.Meanwhile,we suggest an algorithm for fast implementation of the proposed methodology.Finally,we conduct simulations and apply the proposed methods to analyze the peasant uprisings in north China.In chapter 3,based on the proposed weighted composite quantile regression,we use the adaptive-LASSO regularization to simultaneously estimate parameters and select variables.Under regularity conditions,we establish asymptotic properties of the proposed estimators.Simulations suggest that the proposed procedure is more efficient and robust,and a real data analysis is used to illustrate the performance.In chapter 4,we give a summary of the dissertation and outline a future research plan.