Spring 2013 Seminar Series

DATE: 10/31/2013
LOCATION: E51-315
TIME: 4:15pm
Reception immediately following

SPEAKER:
Alex Belloni

TITLE
Uniform Inference After Model Selection

ABSTRACT
We propose robust methods for inference on the effect of a treatment variable on a scalar outcome in the presence of very many controls. Our setting is a partially linear model with possibly non-Gaussian and heteroscedastic disturbances where the number of controls may be much larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by conditioning on a relatively small number of controls whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of controls. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the post-double-selection method. Our results apply to Lasso-type methods used for covariate selection as well as to any other model selection method that is able to find a sparse model with good approximation properties. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We also discuss how to construct new methods to the case of non-linear models (quantile regression and logistic regression). We illustrate the use of the developed methods with numerical simulations and three empirical applicaitons. This talk is based on joint works with Victor Chernozhukov, Chris Hansen, Kengo Kato, and Ying Wei.