High-Dimensional Regression Modeling and Its Application

• Activity Number: 44
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Yuanzhang Li*+ and David W. Niebuhr
• Companies: Walter Reed Army Institute of Research and Walter Reed Army Institute of Research
• Keywords: High dimensional regression ; gradien vector ; multiple imputation ; biomarkers

Abstract

Regression of high dimensional data is particularly difficult when the number of observations is limited. Principal Component Analysis, canonical correlation analysis, factor analysis, etc. are commonly used methods to reduce data dimensions. The goal is usually to find a particular partition of the space X consisting of all independent factors. In this paper, we propose an approach to high dimensional regression for application whether N>k or N< k, where N is the sample size, k is the dimension of space X. The approach starts by finding the most significant linear combination and one of the most insignificant directions to decompose the sample space into two subspaces to reduce the dimension. Then we repeat this process eliminating the independent variables with small contribution to the significant factors to construct space with a fewer independent factors with minimal lose of predict