Asymptotics with Increasing Dimension for Robust Regression with Applications to the Bootstrap

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. A stochastic expansion for M-estimates in linear models with many parameters is derived under the weak condition Kn'/3(log n)2/3 O 0, where n is the sample size and K the maximal diagonal element of the hat matrix. The expansion is used to study the asymptotic distribution of linear contrasts and the consistency of the bootstrap. In particular, it tums out that bootstrap works in cases where the usual asymptotic approach fails.