Statistics Inference with High Dimensional Data

Abstract

Statistical Inference with High-Dimensional Data Cun-Hui Zhang1 1Department of Statistics, Rutgers University, USA ?:? We propose a semi low-dimensional (LD) approach for statistical analysis of certain types of high-dimensional (HD) data. The proposed approach is best described with the following model statement: model = LD component + HD component The main objective of this semi-LD approach is to develop statistical inference procedures for the LD component, including p-values and confidence regions. This semi-LD approach is very much inspired by the semiparametric approach in which a statistical model is decomposed as follows: model = parametric component + nonparametric componentJust as in the semiparametric approach, the worst LD submodel gives the minimum Fisher information for the LD component, along with an efficient score function. The efficient score function, or an estimate of it, can be used to derive an efficient estimator for the LD component. The efficient estimator is asymptotically normal with the inverse of the minimum Fisher information as its asymptotic covariance matrix. This asymptotic covariance matrix may be consistently estimated in a natural way. Consequently, approximate confidence intervals and p-values can be constructed.