期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：02
出版社：Indian Statistical Institute
摘要：We propose a new version of the regression $\alpha$-quantile in the linear regression model, ordering the residuals with respect to an initial R-estimate of the slope parameter. In this way we obtain a consistent estimator of $(\beta_0+F^{-1}(\alpha),\beta_1,\ldots,\beta_p)^{\prime},$ asymptotically equivalent to the regression $\alpha$-quantile of Koenker and Bassett. The result is extended to the extreme regression quantiles. Similarly we construct a version of the autoregression quantile in the linear AR($p$) model. We also propose an estimate of the extreme error in the linear regression and autoregression models, using the initial R-estimate of the slope. A simulation experiment illustrates a very small difference between the original regression quantiles and their new versions, and a very good approximation of the extreme errors.
