Journal article
Power Enhancement in High-Dimensional Cross-Sectional Tests
Econometrica, Vol.83(4), pp.1497-1541
07/2015
DOI: 10.3982/ECTA12749
PMCID: PMC4714420
PMID: 26778846
Abstract
We propose a novel technique to boost the power of testing a high-dimensional vector H:=0 against sparse alternatives where the null hypothesis is violated by only a few components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme value tests, on the other hand, require either stringent conditions or bootstrap to derive the null distribution and often suffer from size distortions due to the slow convergence. Based on a screening technique, we introduce a power enhancement component, which is zero under the null hypothesis with high probability, but diverges quickly under sparse alternatives. The proposed test statistic combines the power enhancement component with an asymptotically pivotal statistic, and strengthens the power under sparse alternatives. The null distribution does not require stringent regularity conditions, and is completely determined by that of the pivotal statistic. The proposed methods are then applied to testing the factor pricing models and validating the cross-sectional independence in panel data models.
Details
- Title: Subtitle
- Power Enhancement in High-Dimensional Cross-Sectional Tests
- Creators
- Jianqing Fan - Princeton UniversityYuan Liao - University of Maryland, College ParkJiawei Yao - Princeton University
- Resource Type
- Journal article
- Publication Details
- Econometrica, Vol.83(4), pp.1497-1541
- DOI
- 10.3982/ECTA12749
- PMID
- 26778846
- PMCID
- PMC4714420
- NLM abbreviation
- Econometrica
- ISSN
- 0012-9682
- eISSN
- 1468-0262
- Publisher
- Wiley
- Number of pages
- 45
- Grant note
- DMS-1206464; DMS-1406266 / National Science Foundation; National Science Foundation (NSF) R01GM100474 / 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) R01GM100474-01; R01-GM072611 / National Institute of Health; United States Department of Health & Human Services; National Institutes of Health (NIH) - USA University of Maryland
- Language
- English
- Date published
- 07/2015
- Academic Unit
- Economics
- Record Identifier
- 9984936837902771
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