Robust linear model selection based on least angle regression

• 成果类型: Article
• 署名作者: Khan, Jafar A.; Van Aelst, Stefan; Zamar, Ruben H.
• 署名单位: University of Dhaka; Ghent University; University of British Columbia
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000000950
• 发表日期: 2007
• 页码: 1289-1299
• 关键词: inference; location

摘要

In this article we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contain anomalies that are difficult to visualize and clean. We want to predict the nonoutlying cases; therefore, we need a method that is simultaneously robust and scalable. We consider the stepwise least angle regression (LARS) algorithm which is computationally very efficient but sensitive to outliers. We introduce two different approaches to robustify LARS. The plug-in approach replaces the classical correlations in LARS by robust correlation estimates. The cleaning approach first transforms the data set by shrinking the outliers toward the bulk of the data (which we call multivariate Winsorization) and then applies LARS to the transformed data. We show that the plug in approach is time-efficient and scalable and that the bootstrap can be used to stabilize its results. We recommend using bootstrapped robustified LARS to sequence a number of candidate predictors to form a reduced set from which a more refined model can be selected.