Robust Winsorized Regression Using Bootstrap Approach

Abstract

The history of regression analysis when response and explanatory variables are subject to error dates back to Eisenhart (1939 Eisenhart , C. ( 1939 ). The interpretation of certain regression methods and their use in biological and industrial research . The Annals of Mathematical Statistics 10 : 162 – 186 .[Crossref] , [Google Scholar]) and Wald (1940 Wald , A. ( 1940 ). The fitting of straight line if both variables are subject to errors . Annals of Mathematical Statistics 11 : 284 – 300 .[Crossref] , [Google Scholar]). Now the subject is discussed in the robust regression framework involving “leverage” points in addition to the traditional “outliers,” e.g., see Rousseeuw and Leroy (1987 Rousseeuw , P. J. , Leroy , A. M. ( 1987 ). Robust Regression and Outlier Detection . New York : John Wiley Sons .[Crossref] , [Google Scholar]). In this article, we develop two variations of co-ordinatewise Winsorized-bootstrapped approach and study their properties using empirical methods and illustrative examples. The new methods are seen to provide significant improvement when the data are in a neighborhood of multivariate normal population without significant loss in the performance when the multivariate normal model holds.