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On minimax cardinal spline interpolation

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  • B. Levit

    (Queen’s University)

Abstract

It is shown that in the problem of cardinal interpolation, spline interpolants of various degrees are R-minimax, with respect to corresponding Sobolev and Hardy functional classes, under restrictions determined by the interference between their oscillating variance and bias. The results raise a natural question: what degrees of interpolating splines are more appropriate, for given Sobolev or Hardy classes? It turns out that the scales of such functional classes can be divided into “very smooth” and “not-so-smooth” subfamilies, whereby “very smooth” classes can benefit from higher degrees of cardinal splines, and vice versa.

Suggested Citation

  • B. Levit, 2022. "On minimax cardinal spline interpolation," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 17-41, April.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:1:d:10.1007_s11203-021-09261-5
    DOI: 10.1007/s11203-021-09261-5
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