Least Absolute Deviation Estimator of Parameter in Regression Analysis for Contamination Data

Consider the simple regression model y_i=x_i^\prime \beta+e_i, i=1, \cdots, n, where \mathrmE e_i=0, \mathrmE e_i^2=\sigma_1^2 Assume that y₁, y₂, …,y_n are contaminated by another i.i.d. random variable variable sequence μ₁,μ₂,...,μ_n and only the contaminated data y_i^*=(1-\nu) y_i+\nu \mu_i are observable, where 0≤v<1 is unknown contaminated parameter. In this paper we give LADE \widehat\beta_n of β by contamination data and establish its asymptotic normality and consistency.