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A family of splines for non-parametric regression and their relationships with kriging. (English) Zbl 0714.62031
Summary: An extension of the theory of polynomial smoothing splines is developed for the statistical problem of estimating a curve based on incomplete and noisy observations. The smoothness of a curve is measured by a quadratic function of its Fourier transform in the space of tempered distributions. These splines, called \(\alpha\)-splines, bring a new connection between smoothing splines estimates and kriging estimates: for the polynomial generalized covariance, the kriging estimate is equivalent to a particular \(\alpha\)-spline.

MSC:
62G07 Density estimation
65D05 Numerical interpolation
62G20 Asymptotic properties of nonparametric inference
65D10 Numerical smoothing, curve fitting
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