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Journal of Statistical Theory and Practice

, Volume 2, Issue 3, pp 465–474 | Cite as

Asymptotic Optimality of Periodic Spline Interpolation in Non-parametric Regression

  • Jaerin Cho
  • Boris Levit
Article

Abstract

A class of interpolation type estimates based on the so-called periodic Lagrange splines is considered. Asymptotic rate optimality of these estimates is established for periodic Sobolev classes. Moreover, it is shown that these estimates are asymptotically optimal to the constant for certain classes of periodic analytic functions. An additional advantage of these estimates is a non-asymptotic upper risk bound which can be used, in principle, with any number of observations.

AMS Subject Classification

Primary 62G08 secondary 65D07 

Keywords

Non-parametric estimation periodic Lagrange spline Sobolev classes analytic functional classes 

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Copyright information

© Grace Scientific Publishing 2008

Authors and Affiliations

  1. 1.Department of System Management EngineeringSungkyunkwan UniversitySuwonKorea
  2. 2.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

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