ON A NEW MODEL ESTIMATION AND TEST FOR HIGH-DIMENSIONAL DATA

Abstract

In this dissertation, we address two topics in high dimensional data analysis and goodness-of-fit test. In the first part of this dissertation, a new method for high dimensional regression and classification is proposed. It uses nonparametric regression to model the relationship between the response and each covariate variable and then use penalized regression method to combine the estimated marginal models. To further improve the flexibility of this method, boosting method is applied to the residuals of previously models. Asymptotic theory and consistency result about the estimation procedure are established.

In the second part, we consider the goodness-of-fit test that is designed to incorporate all relevant information provided by the covariates to the response. Combining a measure of independence and resampling method, we propose a new method for the test. Corresponding asymptotic results are established. We demonstrate numerically the performance of our tests and compare the results with existing relevant methods.