Asymptotic Optimality of Periodic Spline Interpolation in Non-parametric Regression
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 ClassificationPrimary 62G08 secondary 65D07
KeywordsNon-parametric estimation periodic Lagrange spline Sobolev classes analytic functional classes
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