Asymptotic optimality of periodic spline interpolation in non-parametric regression. (English) Zbl 1211.62063

Summary: 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.


62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65D07 Numerical computation using splines
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