Spline Functions and Stochastic Filtering

Thomas-Agnan, Christine

Ann. Statist., Tome 19 (1991) no. 1, p. 1512-1527 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 1991-09-14
Classification:  Spline functions,  interpolation,  smoothing,  partial splines,  inf-convolution splines,  reproducing kernel,  locally homogeneous random fields,  variogram,  kriging,  62M20,  65D07,  62M15