Weak consistency of estimators in linear regres- sion model

Abstract

A linear regression model and M-estimator of its regression coecients
are considered in the paper. We present a derivation of a weak consistency
of the M-estimator together with a rate. Derivation is made under general
conditions set on the error term, say "asymptotic stationarity" property.
The results are proved by means of L2-convergence and cover the cases
as the error term is ARMA, ARCH, GARCH process or it is attracted
by an ARMA, ARCH, GARCH process. We do not separate random and
deterministic covariates. Both cases are treated in one general setting.