Hypothesis Testing for High-Dimensional Linear Regression with Linear Constraints

• Activity Number: 455
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Pixu Shi*+ and Hongzhe Li
• Companies: University of Pennsylvania and University of Pennsylvania
• Keywords: Compositional data ; High-dimensional regression ; Linear constraints ; Log-contrast model ; Microbiome ; Scaled Lasso

Abstract

Motivated by research problems stemming from the analysis of compositional microbiome data, we propose a general method for constructing confidence intervals and p-values for high-dimensional linear models with linear constraints. Our method is based on the construction of a de-biased version of the l1 regularized constrained estimator. Theoretical justifications are provided. The performance of our method is evaluated using simulations on high-dimensional log-contrast model, a model designed for compositional data analysis and a special case of high-dimensional linear model with linear constraints. We also apply our method to a microbiome study that relates body mass index to human gut microbiome composition. Three genera of bacteria are identified to be statistically significant at level of 0.05.