Regression Rank Scores and Regression Quantiles

Gütenbrunner, Christoph; Jurečková, Jana

doi:10.1214/aos/1176348524

Cited by 218 publications

(119 citation statements)

References 19 publications

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“…A variety of methods to construct confidence intervals not requiring density estimation are available. They include the inversion of rank-tests (Gutenbrunner & Jurečková (1992) and Gutenbrunner et al (1993)), a range of resampling methods (Parzen, Wei, & Ying (1994)), Markov Chain Marginal Bootstrap (Hu & He (2012)), jackknife (Portnoy (2014)), and a "direct" method by Zhou & Portnoy (1996).…”

Section: Introductionmentioning

confidence: 99%

Saddlepoint tests for quantile regression

Ronchetti

Sabolová

2016

Can J Statistics

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Quantile regression is a flexible and powerful technique which allows to model the quantiles of the conditional distribution of a response variable given a set of covariates. Regression quantile estimators can be viewed as M −estimators and standard asymptotic inference is readily available based on likelihoodratio, Wald, and score-type test statistics. However, these statistics require the estimation of the sparsity function s(α) = [g(G −1 (α))] −1 , where G and g are the cumulative distribution function and the density of the regression errors respectively, and this can lead to nonparametric density estimation. Moreover, the asymptotic χ 2 distribution for these statistics can provide an inaccurate approximation of tail probabilities and this can lead to inaccurate p-values, especially for moderate sample sizes. Alternative methods which do not require the estimation of the sparsity function, include rank techniques and resampling methods to obtain confidence intervals, which can be inverted to test hypotheses. These are typically more accurate than the standard M − tests.In this paper we show how accurate tests can be obtained by using a nonparametric saddlepoint test statistic. The proposed statistic is asymptotically χ 2 distributed, does not require the specification of the error distribution, and does not require the estimation of the sparsity function. The validity of the method is demonstrated through a simulation study, which shows both the robustness and the accuracy of the new test compared to the best available alternatives.The Canadian Journal of , où G et g sont la fonction de répartition et la fonction de densité des erreurs respectivement et ceci demande de l'estimation nonparamétrique. En plus la distribution asymptotique χ 2 de ces statistiques peut donner lieuà des approximations peu précises des probabilités dans les queues de la distribution et ceci peut produire des p−valeurs imprécises surtout dans le cas d'échantillons de taille moyenne. Des méthodes alternatives qui ne nécessitent pas de l'estimation de la fonction de "sparsity" sont disponibles, par exemple les méthodes de rang et celles de reéchantillonage pour obtenir des intervalles de confiance qui peuventêtre inversés afin de construire des tests. Ces méthodes sont typiquement plus précises que les M −tests standard.Dans cet article on présente une statistique nonparamétrique de pointe de selle qui permet de construire des tests très précis. Elle est asymptotiquement distribuée selon une loi du χ 2 et elle ne nécessite ni de la spécification de la distribution des erreurs ni de l'estimation de la fonction de "sparsity". La performance de la méthode est démontrée par uneétude de simulation, qui montre la robustesse et la précision du nouveau test en comparaison avec les meilleures alternatives disponibles dans la littérature.La revue canadienne de statistique xx: 1-29;

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Section: Introductionmentioning

confidence: 99%

Saddlepoint tests for quantile regression

Ronchetti

Sabolová

2016

Can J Statistics

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“…Bassett and Koenker (1978) showed efficiency of median regression, when the median is more efficient than the mean in a location model. To overcome the restriction of iid errors in linear quantile regression, Gutenbrunner and Jurečková (1992), Koenker and Zhao (1994), and He (1997) developed heterogeneous error models. A comprehensive review is provided in Koenker (2005).…”

Section: Introductionmentioning

confidence: 99%

Efficient quantile regression for heteroscedastic models

Jung

Lee

MacEachern

2014

Journal of Statistical Computation and Simulation

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Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2012) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric ℓ 2 adjustment of the loss function around zero. We extend the idea of ℓ 2 adjusted quantile regression to linear heterogeneous models. The ℓ 2 adjustment is constructed to diminish as sample size grows. Conditions to retain consistency properties are also provided.

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“…The asymptotic distribution of regression quantiles and of regression rank scores under n → ∞ was studied by more authors, under various conditions on f and on the regressors [let us mention Koenker and Bassett (1978), Ruppert and Carroll (1980), Gutenbrunner and Jurečková (1992), Gutenbrunner et al (1993), among others]. The asymptotic properties of autoregression quantiles and the rank scores was studied by Koul and Saleh (1995).…”

Section: Introductionmentioning

confidence: 99%

“…e.g. Gutenbrunner and Jurečková (1992), Gutenbrunner et al (1993)). Moreover, the asymptotic distribution, which is typically normal, does not provide the full information on the behavior ofβ(α), and it can stretch its true behavior under heavy-tailed f.…”

Section: Introductionmentioning

confidence: 99%

Finite-sample distribution of regression quantiles

Jurečková

2010

Statistics & Probability Letters

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The finite sample distributions of the regression quantile and of the extreme regression quantile are derived for a broad class of distributions of the model errors, even for the non-i.i.d case. The distributions are analogous to the corresponding distributions in the location model; this again confirms that the regression quantile is a straightforward extension of the sample quantile. As an application, the tail behavior of the regression quantile is studied.

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Regression Rank Scores and Regression Quantiles

Cited by 218 publications

References 19 publications

Saddlepoint tests for quantile regression

Saddlepoint tests for quantile regression

Efficient quantile regression for heteroscedastic models

Finite-sample distribution of regression quantiles

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