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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.

62G07 Density estimation
65D05 Numerical interpolation
62G20 Asymptotic properties of nonparametric inference
65D10 Numerical smoothing, curve fitting
Full Text: DOI
[1] DOI: 10.1007/BF02170998 · Zbl 0197.13501
[2] DOI: 10.5802/aif.55 · Zbl 0065.09903
[3] DOI: 10.1007/BF01036069
[4] DOI: 10.1214/aoms/1177697089 · Zbl 0193.45201
[5] Kimeldobf G., Sankhya, Ser. A 32 pp 173– (1970)
[6] DOI: 10.1016/0022-247X(71)90184-3 · Zbl 0201.39702
[7] DOI: 10.2307/1425829 · Zbl 0324.60036
[8] Mathebon G., Splines and Kriging their: formal equivalence. In: Syracuse University Geology Contribution B (1981)
[9] Meingtjet , J. 1979.An Intrinsic Approach to Multivariate Spline Interpolation at arbitrary points. In: Polynomial and Spline Approximation, NATO Advances Study Institute Series, Ser. C, 163–190. SAHNEY: BADBI.
[10] DOI: 10.1214/aoms/1177704840 · Zbl 0107.13801
[11] Salkauskas K., Multivariate Approximation Theory II, International Series of Numerical Mahematics 61 (1982)
[12] Schwartz L., Theorie des distributions (1966)
[13] Thomas-agnan C., Statistical Curve fitting by fourier Techniques (1987)
[14] DOI: 10.1137/0911027 · Zbl 0699.65095
[15] Wahba G., JESS B 3 pp 634– (1978)
[16] DOI: 10.1175/1520-0493(1980)108<1122:SNMMFV>2.0.CO;2
[17] Watson G.S., Smoothing and Interpolation by Kriging and with Splines (1983)
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