Weak consistency of estimators in linear regression model

Abstract

We consider behaviour of M-estimators of regression coefficients. A simple derivation of its weak consistency is presented together with a rate of consistency.

Derivation is made under general asymptotic stationary conditions required on the error term. The L2-convergence is the main tool for proving the statements.

Our results cover the cases of ARMA, ARCH, GARCH, etc. error term. Also cases if the error term is attracted to ARMA, ARCH, GARCH process are covered with the paper.

Moreover, investigation of random and deterministic covariates is done in one general scheme. These two cases are not separated.

Keywords

• Estimator
• linear regression model
• weak consistency
• rate of consistency
• L2-convergence