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June 2014 Endogeneity in high dimensions
Jianqing Fan, Yuan Liao
Ann. Statist. 42(3): 872-917 (June 2014). DOI: 10.1214/13-AOS1202

Abstract

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized regression methods is given, which allows us to prove formally the inconsistency claim. To cope with the incidental endogeneity, we construct a novel penalized focused generalized method of moments (FGMM) criterion function. The FGMM effectively achieves the dimension reduction and applies the instrumental variable methods. We show that it possesses the oracle property even in the presence of endogenous predictors, and that 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.

Citation

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Jianqing Fan. Yuan Liao. "Endogeneity in high dimensions." Ann. Statist. 42 (3) 872 - 917, June 2014. https://doi.org/10.1214/13-AOS1202

Information

Published: June 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1246.62153
MathSciNet: MR3210990
Digital Object Identifier: 10.1214/13-AOS1202

Subjects:
Primary: 62F12
Secondary: 62J02 , 62J12 , 62P20

Keywords: conditional moment restriction , endogenous variables , Estimating equation , Focused GMM , global minimization , oracle property , over identification , Semiparametric efficiency , sparsity recovery

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • June 2014
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