an:05879684
Zbl 1211.62063
Cho, Jaerin; Levit, Boris
Asymptotic optimality of periodic spline interpolation in non-parametric regression
EN
J. Stat. Theory Pract. 2, No. 3, 465-474 (2008).
00233250
2008
j
62G08 62G20 65D07
non-parametric estimation; periodic Lagrange spline; Sobolev classes; analytic functional classes
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.