Abstract
A discrete version of the spline smoothing technique is developed to deal with curve estimation problems when the errors have stationary, but not necessarily independent stochastic structure. Both autoregressive and moving average error structures are considered. The use of band matrix manipulations makes it possible to construct linear time algorithms in both cases.
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References
BOX, G.E.P. and JENKINS, G.M. (1976), Time series analysis. Forecasting and control. 2nd edition, Holden-Day, San Francisco.
DIGGLE, P.J. and HUTCHINSON, M.F. (1987), On spline smoothing with autocorrelated errors. CSIRO Technical Report.
GALBRAITH, R.F. and GALBRAITH, J.I. (1974), On the inverses of some patterned matrices arising in the theory of stationary time series. J Appl Prob 11, 63–71.
HARVEY, A.C. (1981), The econometric analysis of time series. Allan, Oxford.
MARTIN, R.S. and WILKINSON, J.H. (1965), Symmetric decomposition of positive definite band matrices. Numer Math 7, 355–361.
SCHIMEK, M.G. and KATSCHNIG, H. (1988), Die Entgiftung des Wiener Stadtgases — eine quasiexperimentelle Evaluation einer suizidpräventiven Maßnahme mittels nichtparametrischer Splineregression. ZSI 17, 293–320.
SILVERMAN, B.W. (1984), Spline smoothing: The equivalent variable kernel method. Annals Stat 12, 898–916.
SILVERMAN, B.W. (1985), Some aspects of the spline smoothing approach to non-parametric regression curve fitting. JRSS B 47, 1–52 (with discussion).
WECKER, W.E. and ANSLEY, C.F. (1983), The signal extraction approach to nonlinear regression and spline smoothing. JASA 78, 81–89.
WHABA, G. (1975), Smoothing noisy data with spline function-s. Numer Math 24, 383–393.
WHABA, G. (1978), Improper priors, spline smoothing and the problem of guarding against model errors in regression. JRSS B 40, 364–372.
WISE, J. (1955), The autocorrelation function and the spectral density function. Biometrika 42, 151–159.
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© 1988 Physica-Verlag Heidelberg
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Schimek, M.G. (1988). A Roughness Penalty Regression Approach for Statistical Graphics. In: Edwards, D., Raun, N.E. (eds) Compstat. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46900-8_4
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DOI: https://doi.org/10.1007/978-3-642-46900-8_4
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0411-9
Online ISBN: 978-3-642-46900-8
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