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On optimal prediction for stochastic processes

โœ Scribed by S.R. Adke; T.V. Ramanathan

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
332 KB
Volume
63
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

The problem of prediction is concerned with predicting an unobserved random variable using a data dependent statistic. We extend the Rao-Blackwell theorem of Johansson (Stand. J. Stati~t. (1990) 17, 135 145) in the prediction context to an arbitrary convex loss function. Two situations in which the problem of obtaining an unbiased predictor with minimum mean squared error of prediction can be reduced to UMVU estimation of an appropriate parametric function arc described. The inadequacy of Rao-Blackwellization of an unbiased predictor when the prediction sufficient statistic is not complete is illustrated with two examples. @ 1997 Elsevier Science B.V.

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โœ Qi Xiao-Jiang ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 720 KB

This paper is concerned with the adaptive prediction for stochastic processes with abruptly changing parameters modelled as a finite-state Markov chain. The Markov transition matrix is assumed to be known. For the coloured noise disturbance case, it is shown that the optimal prediction algorithm req