EMPIRICAL REGRESSION QUANTILE AND LEVERAGE TREATMENT METHOD

Abstract

This article presents analytical and numerical approaches for statistically testing parameter estimates of a regression hyperplane, using Empirical Regression Quantile (ERQ) technique. The analytical approach uses its asymptotic property of ERQ to determine the standard error of parameter estimates. The asymptotical results are replaced and compared with a computer intensive technique referred to as "a bootstrap method." Furthermore, Leverage Treatment, Method (LTM) is proposed for dealing with a leverage point problem that may seriously affect ERQ results. It is not trivial to detect the leverage point in a multivariate date set. An important feature of the LTM is that, it fully utilizes dual variables derived from ERQ for identifying the leverage point. The proposed ERQ/LTM is applied to two illustrative examples in which the technique is compared with other conventional methods.