On minimax cardinal spline interpolation

B. Levit ()
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B. Levit: Queen’s University

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 1, No 3, 17-41

Abstract: 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.

Keywords: Cardinal interpolation; B-splines; Perfect Euler splines; Exponential Euler splines; Fundamental interpolating functions; Interference; Functional classes; Primary 62G08; Secondary 62K05; 33E05; 42A15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09261-5

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