Asymptotic behavior of regression quantiles in non-stationary, dependent cases

Regression quantiles provide a natural and powerful approach for robust analysis of the general linear model. However, departures from independence and stationarity of the errors can have an extremely potent effect on statistical analysis. Here, a Bahadur representation for regression quantiles is provided for error processes which are highly non-stationary (i.e., for which there is a nonvanishing bias term) and which are close to being m-dependent. The conditions for dependence are based on a decomposition of Chanda, Puri, and Ruymgaart which covers linear processes; and, hence, includes ARMA processes.