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Robust Regression Using Data Partitioning and M-Estimation

Authors
Park, YousungKim, DaeyoungKim, Seongyong
Issue Date
1-9월-2012
Publisher
TAYLOR & FRANCIS INC
Keywords
Breakdown point; Data partition; Leverage points; Outlier
Citation
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, v.41, no.8, pp.1282 - 1300
Indexed
SCIE
SCOPUS
Journal Title
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Volume
41
Number
8
Start Page
1282
End Page
1300
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/107478
DOI
10.1080/03610918.2011.598994
ISSN
0361-0918
Abstract
We propose a new robust regression estimator using data partition technique and M estimation (DPM). The data partition technique is designed to define a small fixed number of subsets of the partitioned data set and to produce corresponding ordinary least square (OLS) fits in each subset, contrary to the resampling technique of existing robust estimators such as the least trimmed squares estimator. The proposed estimator shares a common strategy with the median ball algorithm estimator that is obtained from the OLS trial fits only on a fixed number of subsets of the data. We examine performance of the DPM estimator in the eleven challenging data sets and simulation studies. We also compare the DPM with the five commonly used robust estimators using empirical convergence rates relative to the OLS for clean data, robustness through mean squared error and bias, masking and swamping probabilities, the ability of detecting the known outliers, and the regression and affine equivariances.
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