Bahadur-Kiefer representations for GM-estimators in linear Markov models with errors in variables

Abstract

We consider a class of generalized M(GM)-estimators for the autoregressive parameter in a linear Markov model with errors in variables. We show, under some minimal regularity assumptions, that these estimators have almost sure representations of the Bahadur-Kiefer type and consequently they are consistent and asymptotically normal.Errors in variables Linear Markov scheme Almost sure convergence Bahadur-Kiefer type