Jackknife model averaging for high-dimensional quantile regression.

In this paper, we propose a frequentist model averaging method for quantile regression with high-dimensional covariates. Although research on these subjects has proliferated as separate approaches, no study has considered them in conjunction. Our method entails reducing the covariate dimensions through ranking the covariates based on marginal quantile utilities. The second step of our method implements model averaging on the models containing the covariates that survive the screening of the first step. We use a delete-one cross-validation method to select the model weights, and prove that the resultant estimator possesses an optimal asymptotic property uniformly over any compact (0,1) subset of the quantile indices. Our proof, which relies on empirical process theory, is arguably more challenging than proofs of similar results in other contexts owing to the high-dimensional nature of the problem and our relaxation of the conventional assumption of the weights summing to one. Our investigation of finite-sample performance demonstrates that the proposed method exhibits very favorable properties compared to the least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalized regression methods. The method is applied to a microarray gene expression data set.

A varying-coefficient partially linear transformation model for length-biased data with an application to HIV vaccine studies.

Prevalent cohort studies in medical research often give rise to length-biased survival data that require special treatments. The recently proposed varying-coefficient partially linear transformation (VCPLT) model has the virtue of providing a more dynamic content of the effects of the covariates on survival times than the well-known partially linear transformation (PLT) model by allowing flexible interactions between the covariates. However, no existing analysis of the VCPLT model has considered length-biased sampling. In this paper, we consider the VCPLT model when the data are length-biased and right censored, thereby extending the reach of this flexible and powerful tool. We develop a martingale estimating function-based approach to the estimation of this model, provide theoretical underpinnings, evaluate finite sample performance via simulations, and showcase its practical appeal via an empirical application using data from two HIV vaccine clinical trials conducted by the U.S. National Institute of Allergy and Infectious Diseases.

Smoothed Rank Regression for the Accelerated Failure Time Competing Risks Model with Missing Cause of Failure.

This paper examines the accelerated failure time competing risks model with missing cause of failure using the monotone class rank-based estimating equations approach. We handle the non-smoothness of the rank-based estimating equations using a kernel smoothed estimation method, and estimate the unknown selection probability and the conditional expectation by non-parametric techniques. Under this setup, we propose three methods for estimating the unknown regression parameters based on 1) inverse probability weighting, 2) estimating equations imputation and 3) augmented inverse probability weighting. We also obtain the associated asymptotic theories of the proposed estimators and investigate the estimators' small sample behaviour in a simulation study. A direct plug-in method is suggested for estimating the asymptotic variances of the proposed estimators. A real data application based on a HIV vaccine efficacy trial study is considered.