On Edgeworth expansion and moving block bootstrap for studentized M-estimators in multiple linear regression models

This paper considers the multiple linear regression model Y-i = x'(i) beta + epsilon(i), i = i,...,n, where x(i)'s are known p x 1 vectors, beta is a p x 1 vector of parameters, and epsilon(1), epsilon(2),... are stationary, strongly mixing random variables. Let <(beta)over bar (n)> denote an M-estimator of p corresponding to some score function psi. Under some conditions on psi, xi's and Ei's, a two-term Edgeworth expansion for Studentized multivariate M-estimator is proved. Furthermore, it is shown that the moving block bootstrap is second-order correct for some suitable bootstrap analog of Studentized <(beta)over bar (n)>. (C) 1996 Academic Press, Inc.