LAUSR

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.