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.

Keywords:

• Asymptotic normality
• strong consistency
• M estimtors
• linear model
• φ-mixing random variables

Mathematics Subject Classifications:

• 60F05
• 62F12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the National Social Science Foundation of China (22BTJ059), the National Natural Science Foundation of China (12201079, 12201004), the Natural Science Foundation of Anhui Province (2108085QA15, 1908085QA01, 2108085MA06), the Provincial Natural Science Research Project of Anhui Colleges (KJ2021A1095), the Outstanding Top-notch Talent Cultivation Project of Anhui Province (gxgnfx2022073) and the Excellent Young Talent Support Program Project of Higher Education Institutions of Anhui Province (gxyq2022112).