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 = x¹_iβ + ε_i, i = i, ..., n, where x_i's are known p × 1 vectors, β is a p × 1 vector of parameters, and ε1, ε2, ... are stationary, strongly mixing random variables. Let β_n denote an M-estimator of β corresponding to some score function ψ. Under some conditions on ψ, x_i's and ε_i'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 β_n.