Variable Selection for Generalized Linear Model with Highly Correlated Covariates

The penalized variable selection methods are often used to select the relevant covariates and estimate the unknown regression coefficients simultaneously,but these existing methods may fail to be consistent for the setting with highly correlated covariates.In this paper,the semi-standard partial covariance(SPAC)method with Lasso penalty is proposed to study the generalized linear model with highly correlated covariates,and the consistencies of the estimation and variable selection are shown in high-dimensional settings under some regularity conditions.Some simulation studies and an analysis of colon tumor dataset are carried out to show that the proposed method performs better in addressing highly correlated problem than the traditional penalized variable selection methods.

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.

Treatment recommendation and parameter estimation under single-index contrast function

In this article, we consider a semiparametric model for contrast function which is defined asthe conditional expected outcome difference under comparative treatments. The contrast function can be used to recommend treatment for better average outcomes. Existing approachesmodel the contrast function either parametrically or nonparametrically. We believe our approachimproves interpretability over the non-parametric approach while enhancing robustness overthe parametric approach. Without explicit estimation of the nonparametric part of our model,we show that a kernel-based method can identify the parametric part up to a multiplying constant. Such identification suffices for treatment recommendation. Our method is also extendedto high-dimensional settings. We study the asymptotics of the resulting estimation procedure inboth low- and high-dimensional cases. We also evaluate our method in simulation studies andreal data analyses.