Post-Selection Inference for Generalized Linear Models with Many Controls

• Activity Number: 666
• Type: Invited
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: WNAR
• Author(s): Alexandre Belloni* and Victor Chernozhukov and Ying Wei
• Companies: Duke University and MIT and Columbia University
• Keywords: inference after model selection ; generalized linear models ; moment condition models ; Lasso and Post-Lasso with functional response data ; propensity score

Abstract

This paper considers generalized linear models in the presence of many controls. We lay out a general methodology to estimate an effect of interest based on the construction of an instrument that immunize against model selection mistakes and apply it to the case of logistic binary choice model. We propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest $\alpha_0$, a parameter in front of the regressor of interest, such as the treatment variable or a policy variable. These methods allow to estimate $\alpha_0$ at the root-$n$ rate when the total number $p$ of other regressors exceed the sample size $n$, using sparsity assumptions. The estimators and these resulting confidence regions are valid uniformly over $s$-sparse models. Moreover, these procedures are robust with respect to ``moderate" model selection mistakes in variable selection steps. Moreover, the estimators are semi-parametrically efficient in the sense of attaining the semi-parametric efficiency bounds for the class of models in this paper.