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The use of prior information in the estimation of the optimal interpolator parameter

Published online by Cambridge University Press:  14 July 2016

Paul V. Kabaila
Paul V. Kabaila*
Affiliation:
CSIRO Division of Mathematics and Statistics, Melbourne
*
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 310, South Melbourne, Victoria 3205, Australia.
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Abstract

We consider the estimation of the parameter of the best interpolator from a restricted class of linear, time-invariant interpolators for the weakly stationary process {xt}. The estimation is supposed to be based on a part-realisation x1, · ··, xn and on certain prior information regarding the spectral density of the process. Two methods of estimation are proposed — one which uses x1, · ··, xn and the prior information and another which uses only x1, · ··, xn. For the methods proposed it is reasonable to conjecture that the method which utilises the prior information as well as x1, · ··, xn, will be more efficient. Reasonable as this conjecture may seem, its proof is by no means obvious and is the main subject of the paper.

Keywords

TIME-SERIESINTERPOLATIONESTIMATION EFFICIENCY
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 302 - 308
Copyright
Copyright © Applied Probability Trust 

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References

[1] Hannan, E. J. and Heyde, C. C. (1972) On limit theorems for quadratic forms of discrete time series. Ann. Math. Statist. 43, 2058–2068.CrossRefGoogle Scholar
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[3] Kabaila, P. V. and Goodwin, G. C. (1980) On the estimation of the parameter of an optimal interpolator when the class of interpolators is restricted. SIAM J. Control and Optimisation 18, 121–144.CrossRefGoogle Scholar