A two-sample test for the error distribution in nonparametric regression based on the characteristic function

  • G. I. Rivas-Martínez
  • M. D. Jiménez-GameroEmail author
  • J. L. Moreno-Rebollo
Regular Article


A test for the equality of error distributions in two nonparametric regression models is proposed. The test statistic is based on comparing the empirical characteristic functions of the residuals calculated from independent samples of the models. The asymptotic null distribution of the test statistic cannot be used to estimate its null distribution because it is unknown, since it depends on the unknown common error distribution. To approximate the null distribution, a weighted bootstrap estimator is studied, providing a consistent estimator. The finite sample performance of this approximation as well as the power of the resulting test are evaluated by means of a simulation study. The procedure can be extended to testing for the equality of \(d>2\) error distributions.


Two-sample problem Empirical characteristic function Regression residuals Weighted bootstrap Consistency 

Mathematics Subject Classification

62G08 62G10 62G09 



The authors thank the anonymous referees for their constructive comments and suggestions which helped to improve the presentation. G.I. Rivas-Martínez acknowledges financial support from Fundación Carolina, Universidad Nacional de Asunción and Universidad de Sevilla. M.D. Jiménez-Gamero acknowledges financial support from grant MTM2014-55966-P of the Spanish Ministry of Economy and Competitiveness.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Laboratorio de Sistemas de Potencia y ControlUniversidad Nacional de AsunciónSan LorenzoParaguay
  2. 2.Departamento de Estadística e Investigación OperativaUniversidad de SevillaSevilleSpain

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