DIMENSION ASYMPTOTICS FOR GENERALISED BOOTSTRAP IN LINEAR REGRESSION

SNIGDHANSU CHATTERJEE^{1} AND ARUP BOSE^{2}

1^{1}Department of Mathematics and Statistics, University of Nebraska-Lincoln, 924 Oldfather Hall, P.O. Box 880323, Lincoln, NE 68588-0323, U.S.A., e-mail: schatterjee@math.unl.edu 2Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700035, India, e-mail: abose@isical.ac.in

(Received May 17, 1999; revised May 29, 2000)

Abstract. We prove consistency of a class of generalised bootstrap techniques for the distribution of the least squares parameter estimator in linear regression, when the number of parameters tend to infinity with data size and the regressors are random. We show that best results are obtainable with resampling techniques that have not been considered earlier in the literature.

Key words and phrases: Bootstrap, jackknife, regression, dimension asymptotics.