Conference on High-Dimensional Statistics

High-Dimensional Statistics has grown out of modern research activities in diverse fields such as science, technology, and business, aided by powerful computing. It encompasses several emerging fields in statistics such as high-dimensional inference, dimension reduction, data mining, machine learning, and bioinformatics.

Jianqing Fan

Title of Talk: Endogeneity in Ultra High Dimensional Models

Abstract: Most papers on high-dimensional statistics are based on the assumption that one of the regressors are correlated with the regression error, namely, they are exogeneous. Yet, endogeneity arises easily in high-dimensional regression due to a large pool of regressors and this causes the inconsistency of the penalized least-squares methods. A necessary condition for model selection of a very general class of penalized regression methods is given, which allows us to prove formally the inconsistency claim. To cope with the possible endogeneity, we construct a novel penalized generalized method of moments (PGMM) criterion function and offer a new optimization algorithm. The PGMM is not a smooth function. To establish its asymptotic properties, we first study the model selection consistency and an oracle property for a general class of penalized regression methods. These results are then used to show that the PGMM possesses an oracle property even in presence of endogenous predictors, the solution is also near global minimum under the over-identification assumption. Finally, we also show how the semi-parametric efficiency of estimation can be achieved via a two-step approach. (Joint with Yuan Liao)