{"title":"Cluster-based L2 re-weighted regression","authors":"Ekele Alih, Hong Choon Ong","doi":"10.1016/j.stamet.2015.05.005","DOIUrl":null,"url":null,"abstract":"<div><p>A simple robust <span><math><mi>L</mi><mn>2</mn></math></span>-regression estimator is presented.<!--> <!-->The proposed method blends a minimum covariance determinant <span><math><mrow><mo>(</mo><mi>M</mi><mi>C</mi><mi>D</mi><mo>)</mo></mrow></math></span> concentration algorithm with a controlled ordinary least squares regression phase.<!--> <!-->A hierarchical cluster analysis then partitions the data into main cluster of “half set”<!--> <!-->and a minor cluster of one or more groups.<!--> <!-->An initial least squares regression estimate arises from the main cluster of “half set”.<!--> <!-->Thereafter, a group-additive difference in fit statistic is used to activate the minor cluster and a controlled re-weighted least squares regression yields a robust efficient estimator with high breakdown value.<!--> <!-->Simulation experiment shows the advantage of the proposed method over the popular robust regression techniques in terms of robustness of coefficients, and blending outlier diagnostic procedure with parameter estimation.</p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"27 ","pages":"Pages 51-81"},"PeriodicalIF":0.0000,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.05.005","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312715000477","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
A simple robust -regression estimator is presented. The proposed method blends a minimum covariance determinant concentration algorithm with a controlled ordinary least squares regression phase. A hierarchical cluster analysis then partitions the data into main cluster of “half set” and a minor cluster of one or more groups. An initial least squares regression estimate arises from the main cluster of “half set”. Thereafter, a group-additive difference in fit statistic is used to activate the minor cluster and a controlled re-weighted least squares regression yields a robust efficient estimator with high breakdown value. Simulation experiment shows the advantage of the proposed method over the popular robust regression techniques in terms of robustness of coefficients, and blending outlier diagnostic procedure with parameter estimation.
期刊介绍：
Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.
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