New Statistical Methods for Drawing Inference Based on High Dimensional Regression Models

Abstract

Quantifying the uncertainty of estimated parameters in high dimensional sparse models gives critical insights and valuable information in analyzing various types of big data. Yet it possesses some unique difficulties and has been drawing numerous research attention over the past years. The goal of high dimensional inference is to provide accurate point estimators of the unknown parameters with tractable limiting distributions, which leads to confidence intervals, significance testing, and other uncertainty measures. In this dissertation, we propose a novel estimation procedure, along with a non-parametric variance estimator, which is adaptive to a wide range of regression models and outcome types to draw reliable inferences for the model parameters. Comparisons are made with several existing methods, and advantages of our procedure are shown both in simulation studies and real data applications. Our method is successfully applied to multiple genomic data sets with continuous, binary, and survival outcomes.