Computation of certain minimum L₂–distance type estimators under the linear model

Abstract

Let {(x_i:, Y_i:), i = 1, …, n) be the observed data, where x_i:is a real vector of length k and Y_i:, i = 1, …, n a sequence of random variables (r.v.'s). The minimum distance (M.D.) estimators considered here are obtained by minimizing with respect to t the integral dH(y) of the R²norm of the following functionals A-^{½ n}[d]_i=1:x_i:{IY_i:-x_i:t[d]y] -I[-Y_i+ x_i:t[d]y]} and A₁:^{½ n}[d]_i=1::(x_i:- x)I[Y_iy + x_it], where A and A_l:are matricies such that the inverse of their square root exists. The existence of some of these estimators of the k-dimensional slope parameters under the multiple linear

Keywords:

• Least squares
• M. estimators