VALID EDGEWORTH EXPANSIONS OF M-ESTIMATORS IN REGRESSION-MODELS WITH WEAKLY DEPENDENT RESIDUALS

Consider a linear regression model y(t) = x(t) beta + u(t), where the u(t)'s are weakly dependent random variables, the x(t)'s are known des ign nonrandom variables, and beta is an unknown parameter. We define a n M-estimator <(beta) over cap(n)> of beta corresponding to a smooth s core function. Then, the second-order Edgeworth expansion for <(beta) over cap(n)> is derived. Here we do not assume the normality of {u(t)} and {u(t)} includes the usual ARMA processes. Second, we give the sec ond-order Edgeworth expansion for a transformation T<(beta over cap(n) )> of <(beta) over cap(n)>. Then, a sufficient condition for T to exti nguish the second-order terms is given. The results are applicable to many statistical problems.