Test of tails based on extreme regression quantiles

The extreme regression quantiles, as analogues of the extreme-order statistics in the linear regression model, were first considered by Smith (1994, Biometrika 81, 173-183) and studied by Portnoy and Jurecková (1999, Extremes, to appear). They may have various important applications, parallel to those of the extreme value theory. We propose the test of the Pareto-type tail with index m, 0<m[less-than-or-equals, slant]m0 of the distribution of errors in the linear regression model, based on the extreme regression quantiles. The asymptotic null distribution of the test criterion is normal and the test is consistent against the Pareto-type tails with a greater index as well as against the exponential (Weibull) tails.