Sampling distribution for a class of estimators for nonregular linear processes

Abstract

Let {Xt; T = 1, 2,...} be a linear process with a location parameter [theta] defined by Xt - [theta] = [Sigma]0[infinity]grZt-r where {Zt; T = 0, ±1,...} is a sequence of independent and identically distributed random variables, with E[short parallel]Z1[short parallel][delta] 0. If [delta] [greater-or-equal, slanted] 1 we assume further than E(Z1) = 0. Let [eta] = [delta] if 0nonregular linear process location parameter linear estimator symmetric stable distribution