González Manteiga, WenceslaoSánchez Sellero, CésarConde Amboage, Mercedes2017-05-232017-05-232017http://hdl.handle.net/10347/15424The main purpose of this dissertation is to collect different innovative statistical methods in quantile regression. The contributions can be summarized as follows: -- A new method to construct prediction intervals involving median regression and bootstrapping the prediction error is proposed. -- A plug-in bandwidth selector for nonparametric quantile regression has been proposed, that is based on nonparametric estimations of the curvature of the quantile regression function and the integrated sparsity. -- Two lack-of-fit tests for quantile regression models have been presented. The first test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates in order to deal with high-dimensional covariates. The second test is based on interpreting the residuals from the quantile model fit as response values of a logistic regression. Then a likelihood ratio test in the logistic regression is used to check the quantile model.engEsta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glQuantile regressionPrediction intervalsBandwidth selectionLack-of-fit testMaterias::Investigación::12 Matemáticas::1209 Estadística::120906 Métodos de distribución libre y no paramétricaMaterias::Investigación::12 Matemáticas::1209 Estadística::120913 Técnicas de inferencia estadísticadoctoral thesisopen access