题目： A High-Dimensional Nonparametric Multivariate Test for Mean Vector
This work is concerned with testing the population mean vector of nonnormal high-dimensional multivariate data. Several tests for high-dimensional mean vector, based on modifying the classical Hotelling T2 test, have been proposed in the literature. Despite their usefulness, they tend to have unsatisfactory power performance for heavy-tailed multivariate data, which frequently arise in genomics and quantitative finance. This paper proposes a novel high-dimensional nonparametric test for the population mean vector for a general class of multivariate distributions. With the aid of new tools in modern probability theory, we proved that the limiting null distribution of the proposed test is normal under mild conditions when the dimension p is substantially larger than the sample size n. We further study the local power of the proposed test and compare its relative efficiency with a modified Hotelling T2 test for high-dimensional data. An interesting finding is that the newly proposed test can have even more substantial power gain with large p than the traditional nonparametric multivariate test does with finite fixed p. We study the finite sample performance of the proposed test via Monte Carlo simulations. We further illustrate its application by an empirical analysis of a genomics data set.
题目： Structure Estimation in the Partially Linear Cox Model
The partially linear Cox model assumes that it is known a priori which covariates have a linear effect and which do not on the log hazards function. However, this is rarely known in practice. We propose a semiparametric pursuit method to simultaneously detect and estimate linear and nonlinear covariate effects on the log hazards function through a penalized group selection method with concave folded penalties. The unknown smoothing functions of the nonlinear component are approximated by the B-splines. Both the parametric and nonparametric estimators are consistent, and the parametric estimator is asymptotically normal. We develop a modified blockwise majorization descent algorithm that is easy to implement and has a fast convergence rate. Simulation studies indicate that the proposed method works well, and the primary biliary cirrhosis data are analyzed for illustration.