Expansion for moments of regression quantiles with applications to nonparametric testing

• Verfasst von: Mammen, Enno [VerfasserIn]
• Verfasst von: Van Keilegom, Ingrid [VerfasserIn]
• Verfasst von: Yu, Kyusang [VerfasserIn]
• Titel: Expansion for moments of regression quantiles with applications to nonparametric testing
• Verf.angabe: Enno Mammen, Ingrid Van Keilegom, Kyusang Yu
• E-Jahr: 2019
• Jahr: 6 March 2019
• Umfang: 35 S.
• Teil: volume:25
• Teil: year:2019
• Teil: number:2
• Teil: pages:793-827
• Teil: extent:35
• Fussnoten: Gesehen am 23.05.2019
• Titel Quelle: Enthalten in: Bernoulli
• Ort Quelle: Aarhus, 1995
• Jahr Quelle: 2019
• Band/Heft Quelle: 25(2019), 2, Seite 793-827
• ISSN Quelle: 1573-9759
• DOI: doi:10.3150/17-BEJ986
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Bahadur expansions
• Sach-SW: goodness-of-fit tests
• Sach-SW: kernel smoothing
• Sach-SW: nonparametric regression
• Sach-SW: nonparametric testing
• Sach-SW: quantiles
• K10plus-PPN: 1666225681

Abstract

We discuss nonparametric tests for parametric specifications of regression quantiles. The test is based on the comparison of parametric and nonparametric fits of these quantiles. The nonparametric fit is a Nadaraya-Watson quantile smoothing estimator. An asymptotic treatment of the test statistic requires the development of new mathematical arguments. An approach that makes only use of plugging in a Bahadur expansion of the nonparametric estimator is not satisfactory. It requires too strong conditions on the dimension and the choice of the bandwidth. Our alternative mathematical approach requires the calculation of moments of Nadaraya-Watson quantile regression estimators. This calculation is done by application of higher order Edgeworth expansions.