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September, 1991 Spline Functions and Stochastic Filtering
Christine Thomas-Agnan
Ann. Statist. 19(3): 1512-1527 (September, 1991). DOI: 10.1214/aos/1176348259


Some relationships have been established between unbiased linear predictors of processes, in signal and noise models, minimizing the predictive mean square error and some smoothing spline functions. We construct a new family of multidimensional splines adapted to the prediction of locally homogeneous random fields, whose "$m$-spectral measure" (to be defined) is absolutely continuous with respect to Lebesgue measure and satisfies some minor assumptions. By considering partial splines, one may include an arbitrary drift in the signal. This type of correspondence underlines the potentialities of cross-fertilization between statistics and the numerical techniques in approximation theory.


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Christine Thomas-Agnan. "Spline Functions and Stochastic Filtering." Ann. Statist. 19 (3) 1512 - 1527, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62092
MathSciNet: MR1126335
Digital Object Identifier: 10.1214/aos/1176348259

Primary: 62M20
Secondary: 62M15 , 65D07

Keywords: inf-convolution splines , interpolation , kriging , locally homogeneous random fields , Partial splines , reproducing kernel , smoothing , Spline functions , variogram

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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