
The Library
High-dimensional influence measure
Tools
Zhao, Junlong, Leng, Chenlei, Li, Lexin and Wang, Hansheng (2013) High-dimensional influence measure. The Annals of Statistics, Volume 41 (Number 5). pp. 2639-2667. doi:10.1214/13-AOS1165 ISSN 0090-5364.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1214/13-AOS1165
Abstract
Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Mathematical statistics, Asymptotic distribution (Probability theory) | ||||
Journal or Publication Title: | The Annals of Statistics | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0090-5364 | ||||
Official Date: | 2013 | ||||
Dates: |
|
||||
Volume: | Volume 41 | ||||
Number: | Number 5 | ||||
Page Range: | pp. 2639-2667 | ||||
DOI: | 10.1214/13-AOS1165 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | National Science Foundation (U.S.) (NSF), Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), National University of Singapore, Fox Ying Tong Education Foundation, Beijing da xue [Peking University], China. Jiao yu bu [Ministry of Education] | ||||
Grant number: | DMS-11-06668 (NSF); 11101022, 11131002, 11271032 (NSFC); |
Request changes or add full text files to a record
Repository staff actions (login required)
![]() |
View Item |