Search

Analyzing the tail quantiles of a response distribution is sometimes more important than analyzing the mean in biomarker studies. Inferences in a quantile regression are complicated when there exist a large number of candidate markers, together with some prespecified controlled covariates. In this study, we develop a new and simple testing procedure to detect the effects of biomarkers in a high-dimensional quantile regression in the presence of protected covariates. The test is based on the maximum-score-type statistic obtained from a conditional marginal regression. We establish the asymptotic properties of the proposed test statistic under both null and alternative hypotheses and propose an alternative multiplier bootstrap method, with theoretical justifications. We use numerical studies to show that the proposed method provides adequate controls of the family-wise error rate with competitive power, and that it can also be used as a stopping rule in a forward regression. The proposed method is applied to a motivating genome-wide association study to detect single nucleotide polymorphisms associated with low glomerular filtration rates in type 1 diabetes patients. [ABSTRACT FROM AUTHOR]

This study examines the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on a quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. This work fills a gap in the literature on extreme quantile regressions, where many important Weibull-type distributions are excluded by the assumed strong conditions. A simulation study shows that the proposed extrapolation method provides estimations of the conditional quantiles of extreme orders that are more efficient and stable than those of the conventional method. The practical value of the proposed method is demonstrated through an analysis of extremely high birth weights. [ABSTRACT FROM AUTHOR]

In many applications, subgroups with different parameters may exist even after accounting for the covariate effects, and it is important to identify the meaningful subgroups for better medical treatment or market segmentation. We propose a robust subgroup identification method based on median regression with concave fusion penalizations. The proposed method can simultaneously determine the number of subgroups, identify the group membership for each subject, and estimate the regression coefficients. Without requiring any parametric distributional assumptions, the proposed method is robust against outliers in the response and heteroscedasticity in the regression error. We develop a convenient algorithm based on local linear approximation, and establish the oracle property of the proposed penalized estimator and the model selection consistency for the modified Bayesian information criteria. The numerical performance of the proposed method is assessed through simulation and the analysis of a heart disease data. [ABSTRACT FROM AUTHOR]

Inference and prediction in quantile regression for longitudinal data are challenging without parametric distributional assumptions. We propose a new semi- parametric approach that uses copula to account for intra-subject dependence and approximates the marginal distributions of longitudinal measurements, given covariates, through regression of quantiles. The proposed method is exible, and it can provide not only efficient estimation of quantile regression coefficients but also prediction intervals for a new subject given the prior measurements and covariates. The properties of the proposed estimator and prediction are established theoretically, and assessed numerically through a simulation study and the analysis of a nursing home data. [ABSTRACT FROM AUTHOR]