Regression Quantiles and Related Processes Under Long Range Dependent Errors

This paper obtains asymptotic representations of the regression quantiles and the regression rank-scores processes in linear regression setting when the errors are a function of Gaussian random variables that ale stationary and long range dependent. These representations are then used to obtain the limiting behavior of L- and linear regression rank-scores statistics based on the above processes. The paper also obtains the asymptotic uniform linearity of the linear regression rank-scores processes and statistics based on residuals under the long range dependent setup. It thus generalizes some of the results of Jurečková [In Proceedings of the Meeting on Nonparametric Statistics and Related topics (A. K. Md. E. Saleh, Ed.) pp. 217-228. Elsevier, Amsterdam/New York] and Gutenbrunner and Jurečková [Ann. Statist. 20 305-329] for the case of independent errors to one of the highly useful dependent errors setup.