Heng Peng

Nonconcave penalized likelihood with a diverging number of parameters

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to ∞ as the sample size increases. Under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators. Furthermore, the consistency of the sandwich formula of the covariance matrix is demonstrated. Nonconcave penalized likelihood ratio statistics are discussed, and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions. The asymptotic results are augmented by a simulation study, and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary.

Two Samples Tests for Functional Data

Data in many experiments arises as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is in terms of functional data analysis (FDA). Functional curves are encountered when units are observed over time. Although the whole function curve itself is not observed, a sufficiently large number of evaluations, as is common with modern recording equipment, is assumed to be available. In this article, we consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which we assume that functional curves are observed, that is, we consider the test if these two groups of curves have the same mean functional curve when the two groups of curves without noise are observed. The L 2-norm based and bootstrap-based test statistics are proposed. It is shown that the proposed methodology is flexible. Simulation study and real-data examples are used to illustrate our techniques.

Smoothed rank correlation of the linear transformation regression model

The maximum rank correlation (MRC) approach is the most common method used in the literature to estimate the regression coefficients in the semiparametric linear transformation regression model. However, the objective function G n ( s ) in the MRC approach is not continuous. The optimization of G n ( s ) requires an extensive search for which the computational cost grows in the order of n d , where d is the dimension of X . Given the lack of smoothing, issues related to variable selection, the variance estimate and other inferences by MRC are not well developed in the model. In this paper, we combine the concept underlying the penalized method, rank correlation and smoothing technique and propose a nonconcave penalized smoothed rank correlation method to select variables and estimate parameters for the semiparametric linear transformation model. The proposed estimator is computationally simple, n 1 / 2 - consistent and asymptotically normal. A sandwich formula is proposed to estimate the variances of the proposed estimates. We also illustrate the usefulness of the methodology with real data from a body fat prediction study.

Estimation of partially linear regression models under the partial consistency property

In this paper, utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate the partially linear model

Estimation and hypothesis test for partial linear multiplicative models

Y=X\beta+g(Z)+\varepsilon

Optimal designs for additive mixture model with heteroscedastic errors

. Motivated by the partial consistency phenomena, we propose to model

Variable Selection for Semiparametric Partially Linear Covariate-Adjusted Regression Models

g(Z)

Tail Probability Ratios of Normal and Student’s t Distributions

via incidental parameters. Based on partitioning the support of

Robust rank correlation based screening

Z

NONCONCAVE PENALIZED M-ESTIMATION WITH A DIVERGING NUMBER OF PARAMETERS

, a simple local average is used to estimate the response surface. The proposed method seeks to strike a balance between computation burden and efficiency of the estimators while minimizing model bias. Computationally this approach only involves least squares. We show that given the inconsistent estimator of