High Dimensional Influence Measure

31 Pages Posted: 29 Aug 2013

See all articles by Junlong Zhao

Junlong Zhao

Beijing Normal University

Chenlei Leng

University of Warwick

Lexin Li

North Carolina State University

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: August 29, 2013

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.

Keywords: Cook's distance, High dimensional diagnosis, Influential observation, Lasso, Marginal correlations, Variable Screening

JEL Classification: C10

Suggested Citation

Zhao, Junlong and Leng, Chenlei and Li, Lexin and Wang, Hansheng, High Dimensional Influence Measure (August 29, 2013). Available at SSRN: https://ssrn.com/abstract=2317649 or http://dx.doi.org/10.2139/ssrn.2317649

Junlong Zhao

Beijing Normal University ( email )

19 Xin Jie Kou street
Beijing 100875
China

Chenlei Leng

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Lexin Li

North Carolina State University ( email )

Hillsborough Street
Raleigh, NC 27695
United States

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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