Strong Consistency of $M$ Estimator in Linear Model for $\widetilde{φ}$-Mixing Samples

Abstract

The strong consistency of $M$ estimator of regression parameter in linear model for $\widetilde{φ}$-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of $M$ estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.