On Edgeworth Expansion and Moving Block Bootstrap for StudentizedM-Estimators in Multiple Linear Regression Models

This paper considers the multiple linear regression modelYi=xi′β+εi,i=i, …, n, wherexiʹs are knownp×1 vectors,βis ap×1 vector of parameters, andε1,ε2, … are stationary, strongly mixing random variables. Letβndenote anM-estimator ofβcorresponding to some score functionψ. Under some conditions onψ,xiʹs andεiʹs, a two-term Edgeworth expansion for Studentized multivariateM-estimator is proved. Furthermore, it is shown that the moving block bootstrap is second-order correct for some suitable bootstrap analog of Studentizedβn.