Hypothesis Testing for High-Dimensional Linear Models

Abstract

This thesis analyses an issue of growing dimension in covariates that often challenges classical Wald-type testing methods (e.g., F-test). Using random matrix theory, we successfully construct the most powerful statistic to be applicable for testing the significance of many coefficients in high-dimensional linear regression model. We enable our test to comprehend some useful features commonly found in large economic and financial datasets such as time dependency structure and volatility clustering. This allows practitioners more flexibility to deal with complicated datasets when the data dimension exceeds its sample size.