Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors.

Koul, Hira L. and Mukherjee, Kanchan (1993) Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors. Probability Theory and Related Fields, 95 (4). pp. 535-553. ISSN 0178-8051

Abstract

This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are Gaussian, or a function of Gaussian random variables, that are strictly stationary and long range dependent. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with long range dependent errors. The latter result, in turn, yields the asymptotic distribution of the Jaeckel (1972) rank estimators. The paper also studies the least absolute deviation and a class of certain minimum distance estimators of regression parameters and the kernel type density estimators of the marginal error density when the errors are long range dependent.