Wild Bootstrap for M Estimators of Linear Regression

• Activity Number: 117
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Xingdong Feng*+ and Xuming He and Jianhua Hu
• Companies: National Institute of Statistical Sciences and University of Illinois at Urbana-Champaign and The University of Texas MD Anderson Cancer Center
• Keywords: Wild bootstrap ; M estimator

Abstract

The wild bootstrap method is capable of accounting for heteroscedasticity in a regression model. However, the existing theory has focused on the wild bootstrap for linear estimators. In this note, we substantially broaden the validity of the wild bootstrap methods by providing a class of weight distributions that yield asymptotically valid wild bootstrap for M estimators of linear regression, including the least absolute deviation estimator and other regression quantile estimators. It is interesting to note that most weight distributions used in the existing wild bootstrap literature lead to biased variance estimates for nonlinear estimators of linear regression, and that for asymmetric loss functions a simple modification of the wild bootstrap admits a broader class of weight distributions. A simulation study on median regression is carried out to compare various bootstrap methods and to demonstrate the relevance of our work in finite-sample problems. With a simple finite-sample correction, the wild bootstrap is shown to be a valuable resampling method to account for general forms of heteroscedasticity in a regression model with fixed design points.