Mathematics – Statistics Theory
Scientific paper
2005-05-30
Annals of Statistics 2005, Vol. 33, No. 2, 806-839
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053604000001165 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053604000001165
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the upper and lower tails. This paper develops a theory of quantile regression in the tails. Specifically, it obtains the large sample properties of extremal (extreme order and intermediate order) quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values. This modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis. In large samples, extreme order regression quantiles converge weakly to \argmin functionals of stochastic integrals of Poisson processes that depend on regressors, while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design.
No associations
LandOfFree
Extremal quantile regression does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Extremal quantile regression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extremal quantile regression will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-314921