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Smoothness and conditioning in generalised smoothing spline calculations

Published online by Cambridge University Press:  17 February 2009

M. R. Osborne  and
Tania Prvan
M. R. Osborne
Affiliation:
Dept. of Statistics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, A.C.T. 2601, Australia.
Tania Prvan
Affiliation:
Dept. of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USA.
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Abstract

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We consider a generalisation of the stochastic formulation of smoothing splines, and discuss the smoothness properties of the resulting conditional expectation (generalised smoothing spline), and the sensitivity of the numerical algorithms. One application is to the calculation of smoothing splines with less than the usual order of continuity at the data points.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 1 , July 1988 , pp. 43 - 56
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Anderson, B. D. O. and Moore, J. B., Optimal Filtering, (Prentice-Hall, Englewood Cliffs 1979).Google Scholar
[2]Ansley, C. F. and Kohn, R., “Estimation, filtering and smoothing in state space models with incompletely specified initial conditions”, Ann. Statist. 13 (1985) 1286–1316.Google Scholar
[3]Duncan, D. B. and Horn, S. D., “Linear dynamic recursive estimation from the viewpoint of regression analysis”, J. Amer. Statist. Assoc. 67 (1972) 816–821.Google Scholar
[4]Gerig, T. M. and Gallant, A. R., “Computing methods for linear models subject to linear constraints”, J. Statist. Comput. Simulation (1975) 283–296.CrossRefGoogle Scholar
[5]Golub, G. H. and VanLoan, C. F., Matrix Computations, (John Hopkins University Press, 1983).Google Scholar
[6]Luenberger, D. G., Optimization by Vector Space Methods, (Wiley, 1969).Google Scholar
[7]Osborne, M. R. and Prvan, Tania, “On algorithms for generalised smoothing splines”, J. Austral. Math. Soc. Ser B 29 (1988) 319–338.Google Scholar
[8]Paige, C. C., “Computer solution and perturbation analysis of generalised linear least squares problems”, Math. Comp. 33 (1979), 171–184.Google Scholar
[9]Paige, C. C. and Saunders, M. A., “Least squares estimation of discrete linear dynamic systems using orthogonal transformations”, SIAM J. Numer. Anal. 14 (1977) 180–193.Google Scholar
[10]Pondit, S. M. and Su, S. M., Time Series and System Analysis with Applications. (Wiley, 1983).Google Scholar
[11]Wecker, W. and Ansley, C. F., “The signal extraction approach to nonlinear regression and spline smoothing”, J. Amer. Statist. Assoc. 78 (1983) 81–89.Google Scholar