Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors

Xin Deng and Xuejun Wang ()
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Xin Deng: Anhui University
Xuejun Wang: Anhui University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1069-1090

Abstract: Abstract In this paper, we first establish a useful result on strong convergence for weighted sums of widely orthant dependent (WOD, in short) random variables. Based on the strong convergence that we established and the Bernstein type inequality, we investigate the strong consistency of M estimators of the regression parameters in linear models based on WOD random errors under some more mild moment conditions. The results obtained in the paper improve and extend the corresponding ones for negatively orthant dependent random variables and negatively superadditive dependent random variables. Finally, the simulation study is provided to illustrate the feasibility of the theoretical result that we established.

Keywords: M estimator; Strong convergence; Strong consistency; Linear model; Widely orthant dependent random errors; 62F12; 60F15 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9589-9

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