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Mathematical Methods of Statistics

, Volume 27, Issue 4, pp 245–267 | Cite as

On Optimal Cardinal Interpolation

  • B. LevitEmail author
Article

Abstract

For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.

In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.

Keywords

cardinal interpolation Optimal Recovery Hardy classes Jacobi elliptic functions infinite Blaschke product interference effect sinc filter 

2000 Mathematics Subject Classification

62G08 secondary 62K05 33E05 42A15 

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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Dept. Math. and Statist.Queen’s Univ.Kingston ONCanada

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