Expansion for moments of regression quantiles with applications to nonparametric testing

被引：2

作者：

Mammen, Enno ^{[1
]}

Van Keilegom, Ingrid ^{[2
]}

Yu, Kyusang ^{[3
]}

机构：

[1] Heidelberg Univ, Inst Angew Math, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[2] Katholieke Univ Leuven, ORSTAT, Naamsestr 69, B-3000 Leuven, Belgium

[3] Konkuk Univ, Dept Appl Stat, Seoul 143701, South Korea

来源：

BERNOULLI | 2019年 / 25卷 / 02期

基金：

欧洲研究理事会;

关键词：

Bahadur expansions; goodness-of-fit tests; kernel smoothing; nonparametric regression; nonparametric testing; quantiles; OF-FIT TEST; BAHADUR REPRESENTATION; STATISTICS; MODELS; MISSPECIFICATION; DERIVATIVES; ESTIMATORS; LINEARITY; INFERENCE;

D O I：

10.3150/17-BEJ986

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：793 / 827

页数：35

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