Zha, Junlong, Li, Chao, Niu, Lu and Leng, Chenlei (2019) Multiple influential point detection in high dimensional regression spaces. Journal of the Royal Statistical Society Series B: Statistical Methodology, 81 (2). pp. 385-408. doi:10.1111/rssb.12311 ISSN 1369-7412.

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Abstract

Influence diagnosis should be routinely conducted when one aims to construct a regression model. Despite its importance, the problem of influence quantification is severely under-investigated in a high-dimensional setting, mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures. Although some progress has been made in recent years, existing approaches are ineffective in detecting multiple influential points especially due to the notorious "masking" and "swamping" effects. To address this challenge, we propose a new group deletion procedure referred to as MIP by introducing two novel quantities named Max and Min statistics. These two statistics have complimentary properties in that the Max statistic is effective for overcoming the masking effect while the Min statistic is useful for overcoming the swamping effect. Combining their strengths, we further propose an efficient algorithm that can detect influential points with prespecified guarantees. For wider applications, we focus on developing the new proposal for the multiple response regression model, encompassing the univariate response linear model as a special case. The proposed influential point detection procedure is simple to implement, efficient to run, and enjoys attractive theoretical properties. Its effectiveness is verified empirically via extensive simulation study and data analysis.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Regression analysis, Robust statistics
Journal or Publication Title:	Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher:	Wiley-Blackwell Publishing, Inc
ISSN:	1369-7412
Official Date:	April 2019
Dates:	Date Event April 2019 Published 1 February 2019 Available 27 December 2018 Accepted
Volume:	81
Number:	2
Page Range:	pp. 385-408
DOI:	10.1111/rssb.12311
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	7 January 2019
Date of first compliant Open Access:	9 April 2019
Funder:	Fundamental Research Funds for the Central Universities
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID 1187110 [NSFC] National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 1147103 [NSFC] National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809 EP/N510129/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266
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