Smooth Estimation of Error Distribution in Nonparametric Regression Under Long Memory

  • Hira L. KoulEmail author
  • Lihong Wang
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 193)


We consider the problem of estimating the error distribution function in a nonparametric regression model with long memory design and long memory errors. This paper establishes a uniform reduction principle of a smooth weighted residual empirical distribution function estimator. We also investigate consistency property of local Whittle estimator of the long memory parameter based on nonparametric residuals. The results obtained are useful in providing goodness of fit test for the marginal error distribution and in prediction under long memory.


Kernel estimation Uniform reduction principle 



Research of Hira L. Koul was in part supported by the NSF-DMS grant 1205271. Research of Lihong Wang was in part supported by NSFC Grants 11671194 and 11171147. Authors are grateful to a delegant referee whose comments helped to improve the presentation and some of the proofs.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

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