Asymptotics of M ‐estimator in multivariate linear regression models for a class of random errors

SummaryIt is known that linear regression models have immense applications in various areas such as engineering technology, economics and social sciences. In this paper, we investigate the asymptotic properties ofM-estimator in multivariate linear regression model based on a class of random errors satisfying a generalised Bernstein-type inequality. By using the generalised Bernstein-type inequality, we obtain a general result on almost sure convergence for a class of random variables and then obtain the strong consistency for theM-estimator in multivariate linear regression models under some mild conditions. The result extends or improves some existing ones in the literature. Moreover, we also consider the case when the dimension $p$ tends to infinity by establishing the rate of almost sure convergence for a class of random variables satisfying generalised Bernstein-type inequality. Some numerical simulations are also provided to verify the validity of the theoretical results.

Source: Australian and New Zealand Journal of Statistics - July 22, 2023 Category: Statistics Authors: Yi Wu, Wei Yu, Xuejun Wang Tags: Original Article Source Type: research