Asymptotic properties of M estimators in classical linear models with φ-mixing random errors

Abstract

In this paper, the asymptotic normality and strong consistency for M estimators of the unknown regression coefficients in classical linear models are established under the assumptions that the errors are identically distributed φ-mixing random variables. The results obtained in this paper generalize the corresponding ones of Chen and Zhao [M-methods in linear model. Shanghai: Scientific and Technical Publishers; 1996] and Zhao [Strong consistency of M-estimates in linear model. Sci China Ser A. 2002;45:1420–1427] for independent errors. Finally, the simulation study is provided to verify the finite sample performance of the theoretical results and a real example is analysed for illustration.