Journal article
ENDOGENEITY IN HIGH DIMENSIONS
The Annals of statistics, Vol.42(3), pp.872-917
06/01/2014
DOI: 10.1214/13-AOS1202
PMCID: PMC4286899
PMID: 25580040
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.
Details
- Title: Subtitle
- ENDOGENEITY IN HIGH DIMENSIONS
- Creators
- Jianqing Fan - Princeton UniversityYuan Liao - University of Maryland, College Park
- Resource Type
- Journal article
- Publication Details
- The Annals of statistics, Vol.42(3), pp.872-917
- DOI
- 10.1214/13-AOS1202
- PMID
- 25580040
- PMCID
- PMC4286899
- NLM abbreviation
- Ann Stat
- ISSN
- 0090-5364
- eISSN
- 2168-8966
- Publisher
- Inst Mathematical Statistics
- Number of pages
- 46
- Grant note
- R01GM100474; R01-GM072611 / National Institute of General Medical Sciences of the National Institutes of Health; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of General Medical Sciences (NIGMS) R01GM072611 / NATIONAL INSTITUTE OF GENERAL MEDICAL SCIENCES; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA; NIH National Institute of General Medical Sciences (NIGMS) DMS-12-06464 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 06/01/2014
- Academic Unit
- Economics
- Record Identifier
- 9984936820902771
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