Regularization Methods for High-Dimensional Instrumental Variables Regression with an Application to Genetical Genomics

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wei Lin*+ and Rui Feng and Hongzhe Li
• Companies: University of Pennsylvania and University of Pennsylvania and University of Pennsylvania
• Keywords: Confounding ; Endogeneity ; Instrumental Variable ; Sparsity ; Two-stage least squares ; Variable selection

Abstract

Motivated by genetical genomics applications where the dimensionality of gene expressions and genetic variants can both be much larger than the sample size, we consider the problem of variable selection and estimation in high-dimensional sparse instrumental variables models. To overcome the difficulty of high dimensionality and unknown optimal instruments, we propose a two-stage regularization framework for identifying and estimating important covariate effects while selecting and estimating optimal instruments. The methodology extends the classical two-stage least squares estimator to high dimensions by exploiting sparsity using sparsity-inducing penalty functions in both stages. In the representative case of $L_1$ regularization, we establish estimation, prediction, and model selection properties of the two-stage regularized estimators in the high-dimensional setting where the dimensions of covariates and instruments are both allowed to grow exponentially with the sample size. The practical performance of the proposed method is evaluated by simulation studies and its usefulness is illustrated by an analysis of mouse obesity data.