Peng Lai

Bias-corrected GEE estimation and smooth-threshold GEE variable selection for single-index models with clustered data

In this paper, we present an estimation approach based on generalized estimating equations and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations, bias-correction is necessary when general working correlation matrices are used in the estimating equations. Our variable selection procedure based on smooth-threshold estimating equations (Ueki (2009) [23]) can automatically eliminate irrelevant parameters by setting them as zeros and is computationally simpler than alternative approaches based on shrinkage penalty. The resulting estimator consistently identifies the significant variables in the index, even when the working correlation matrix is misspecified. The asymptotic property of the estimator is the same whether or not the nonzero parameters are known (in both cases we use the same estimating equations), thus achieving the oracle property in the sense of Fan and Li (2001) [10]. The finite sample properties of the estimator are illustrated by some simulation examples, as well as a real data application.

Quadratic inference functions for partially linear single-index models with longitudinal data

In this paper, we consider the partially linear single-index models with longitudinal data. We propose the bias-corrected quadratic inference function (QIF) method to estimate the parameters in the model by accounting for the within-subject correlation. Asymptotic properties for the proposed estimation methods are demonstrated. A generalized likelihood ratio test is established to test the linearity of the nonparametric part. Under the null hypotheses, the test statistic follows asymptotically a χ2 distribution. We also evaluate the finite sample performance of the proposed methods via Monte Carlo simulation studies and a real data analysis.

Model free feature screening for ultrahigh dimensional data with responses missing at random

The paper concerns the feature screening for the ultrahigh dimensional data with responses missing at random. A model free feature screening procedure based on the inverse probability weighted methods has been proposed, where the Kolmogorov filter method is used to screen the important features under an unknown propensity score function. The suggested screening procedure has several desirable advantages. First, it has property of robust to heavy-tailed distributions of predictors and the presence of potential outliers. Second, it is a model free procedure with mild model assumptions. Third, it can deal with the missing data problem with responses missing at random. Monte Carlo simulation studies are conducted to examine the performance of the proposed procedure and a real data application is also conducted to evaluate and illustrate the proposed methods.

Variable selection and estimation for partially linear single-index models with longitudinal data

In this paper, we consider the partially linear single-index models with longitudinal data. To deal with the variable selection problem in this context, we propose a penalized procedure combined with two bias correction methods, resulting in the bias-corrected generalized estimating equation and the bias-corrected quadratic inference function, which can take into account the correlations. Asymptotic properties of these methods are demonstrated. We also evaluate the finite sample performance of the proposed methods via Monte Carlo simulation studies and a real data analysis.

Semiparametric efficient estimation for partially linear single-index models with responses missing at random

In this paper, we establish the semiparametric efficient bound for the heteroscedastic partially linear single-index model with responses missing at random, and develop an efficient estimating equation method. By solving the estimating equation, we obtain estimators for the parameter vectors in the linear part and the single index part simultaneously. The estimators are asymptotically semiparametrically efficient when the propensity score function is specified correctly. It should be noted that the inverse probability weighted efficient estimating equation cannot be obtained directly from the full data efficient estimating equation by the inverse probability weighted approach. We establish the estimating equation by deriving the observed data efficient score function. Some simulation studies and a real data application were conducted to evaluate and illustrate the proposed methods.

Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model

An efficient estimating equations procedure is developed for performing variable selection and defining semiparametric efficient estimates simultaneously for the heteroscedastic partially linear single-index model. The estimating equations are proposed based on the smooth threshold estimating equations by using the efficient score function of partially linear single-index models. And this estimating equations procedure can be used to perform variable selection without solving any convex optimization problems, and automatically eliminate nonsignificant variables by setting their coefficients as zero. The resulting estimators enjoy the oracle property and are semiparametrically efficient. The finite sample properties of the proposed estimators are illustrated by some simulation examples, as well as a real data application.

Empirical likelihood calibration estimation for the median treatment difference in observational studies

The estimation of average (or mean) treatment effects is one of the most popular methods in the statistical literature. If one can have observations directly from treatment and control groups, then the simple t-statistic can be used if the underlying distributions are close to normal distributions. On the other hand, if the underlying distributions are skewed, then the median difference or the Wilcoxon statistic is preferable. In observational studies, however, each individuals choice of treatment is not completely at random. It may depend on the baseline covariates. In order to find an unbiased estimation, one has to adjust the choice probability function or the propensity score function. In this paper, we study the median treatment effect. The empirical likelihood method is used to calibrate baseline covariate information effectively. An economic dataset is used for illustration.

Partially Linear Structure Selection in Cox Models with Varying Coefficients

To explore the nonlinear interactions between covariates and an index variable, partially linear proportional hazards models have been proposed for censored survival data. However, specification of the partially linear structure was usually carried out in an ad-hoc manner by first fitting a full varying-coefficient model and visually examining the resulting fit to identify the linear part. In this article, we consider the problem of coefficient estimation and constant coefficient identification based on a double shrinkage approach. Variable selection is also considered in a coherent estimation framework, resulting in a double-penalization procedure. Under the mild assumptions, we establish asymptotic properties for the procedure such as consistency, sparesistency, constansistency, and asymptotic normality. We evaluate the performance of the proposed method by numerical simulations and demonstrate its application using a breast cancer data set.

Robust rank screening for ultrahigh dimensional discriminant analysis

In this paper, we consider sure independence feature screening for ultrahigh dimensional discriminant analysis. We propose a new method named robust rank screening based on the conditional expectation of the rank of predictor’s samples. We also establish the sure screening property for the proposed procedure under simple assumptions. The new procedure has some additional desirable characters. First, it is robust against heavy-tailed distributions, potential outliers and the sample shortage for some categories. Second, it is model-free without any specification of a regression model and directly applicable to the situation with many categories. Third, it is simple in theoretical derivation due to the boundedness of the resulting statistics. Forth, it is relatively inexpensive in computational cost because of the simple structure of the screening index. Monte Carlo simulations and real data examples are used to demonstrate the finite sample performance.

Ultrahigh dimensional feature screening via projection

This work is concerned with feature screening for linear model with multivariate responses and ultrahigh dimensional covariates. Instead of utilizing the correlation between every response and covariate, the linear space spanned by the multivariate responses is considered in this paper. Based on the projection theory, each covariate is projected on the linear space spanned by the multivariate responses, and a new screening procedure called projection screening (PS) is proposed. The sure screening and ranking consistency properties are established under some regular conditions. To solve some difficulties in marginally feature screening for linear model and enhance the screening performance of the proposed procedure, an iterative projection screening (IPS) procedure is constructed. The finite sample properties of the proposed procedure are assessed by Monte Carlo simulation studies and a real-life data example is analysed.