Self-Normalized Moderate Deviations for Degenerate -Statistics.

In this paper, we study self-normalized moderate deviations for degenerate -statistics of order 2. Let {Xi,i≥1} be i.i.

ASYMPTOTIC DISTRIBUTIONS OF HIGH-DIMENSIONAL DISTANCE CORRELATION INFERENCE.

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped.

ARE DISCOVERIES SPURIOUS? DISTRIBUTIONS OF MAXIMUM SPURIOUS CORRELATIONS AND THEIR APPLICATIONS.

Over the last two decades, many exciting variable selection methods have been developed for finding a small group of covariates that are associated with the response from a large pool. Can the discoveries by such data mining approaches be spurious due to high dimensionality and limited sample size? Can our fundamental assumptions on exogeneity of covariates needed for such variable selection be validated with the data? To answer these questions, we need to derive the distributions of the maximum spurious correlations given certain number of predictors, namely, the distribution of the correlation of a response variable with the best linear combinations of covariates , even when and are independent. When the covariance matrix of possesses the restricted eigenvalue property, we derive such distributions for both finite and diverging , using Gaussian approximation and empirical process techniques.

Maximum Likelihood Inference for the Cox Regression Model with Applications to Missing Covariates.

In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model (Cox, 1972, 1975) both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.