Yazhao Lv

A robust and efficient estimation method for single index models

Single index models are natural extensions of linear models and overcome the so-called curse of dimensionality. They have applications to many fields, such as medicine, economics and finance. However, most existing methods based on least squares or likelihood are sensitive when there are outliers or the error distribution is heavy tailed. Although an M-type regression is often considered as a good alternative to those methods, it may lose efficiency for normal errors. In this paper, we propose a new robust and efficient estimation procedure based on local modal regression for single index models. The asymptotic normality of proposed estimators for both the parametric and nonparametric parts is established. We show that the proposed estimators are as asymptotically efficient as the least-square-based estimators when there are no outliers and the error distribution is normal. A modified EM algorithm is presented for efficient implementation. The simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed method.

Variable selection for varying dispersion beta regression model

The beta regression models are commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). In this paper, we consider the issue of variable selection for beta regression models with varying dispersion (VBRM), in which both the mean and the dispersion depend upon predictor variables. Based on a penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. Following the coordinate descent algorithm idea of generalized linear models, we develop new variable selection procedure for the VBRM, which can efficiently simultaneously estimate and select important variables in both mean model and dispersion model. Simulation studies and body fat data analysis are presented to illustrate the proposed methods.

Quantile regression and variable selection for the single-index model

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.

Semi Varying Coefficient Zero-Inflated Generalized Poisson Regression Model

In this paper, the semi varying coefficient zero-inflated generalized Poisson model is discussed based on penalized log-likelihood. All the coefficient functions are fitted by penalized spline (P-spline), and Expectation-maximization algorithm is used to drive these estimators. The estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. The score test statistics about dispersion parameter is discussed based on the P-spline estimation. Both simulated and real data example are used to illustrate our proposed methods.

Variable selection in partially linear hazard regression for multivariate failure time data

The aim of this paper is to explore variable selection approaches in the partially linear proportional hazards model for multivariate failure time data. A new penalised pseudo-partial likelihood method is proposed to select important covariates. Under certain regularity conditions, we establish the rate of convergence and asymptotic normality of the resulting estimates. We further show that the proposed procedure can correctly select the true submodel, as if it was known in advance. Both simulated and real data examples are presented to illustrate the proposed methodology.

Semiparametric inference on partially linear single-index model

ABSTRACT We consider semiparametric inference on the partially linearsingle-index model (PLSIM). The generalized likelihood ratio (GLR) test is proposed to examine whether or not a family of new semiparametric models fits adequately our given data in the PLSIM. A new GLR statistic is established to deal with the testing of the index parameter α0 in the PLSIM. The newly proposed statistic is shown to asymptotically follow a χ2-distribution with the scale constant and the degrees of freedom being independent of the nuisance parameters or function. Some finite sample simulations and a real example are used to illustrate our proposed methodology.

Variable selection in semiparametric hazard regression for multivariate survival data

This paper is concerned with how to select significant variables in the partially linear varying-coefficient hazard model for multivariate survival data. A new variable selection procedure is proposed to simultaneously estimate the parameters and select variables for the parametric parts. Compared to the profile pseudo-partial likelihood proposed by Cai et?al. (2008), the advantage of our method is to be practically feasible and easily implemented. We show that the estimators of both the parametric and nonparametric parts achieve the best convergence rates and establish their asymptotic normality. Moreover, we demonstrate that proposed procedures perform as well as an oracle procedure. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed procedures and a real dataset from the Colon Cancer Study is analyzed for illustration.