Abstract
Prediction and signal estimation are considered in the class of Gaussian non-deterministic stationary processes. In this class the traditional Minimum Mean Square Error (MMSE) criterion yields the estimator whose distribution is singular with respect to the distribution of the estimated process. Processes with singular probability distributions are discernible by the Bayes test. Different class of estimators is obtained when instead of the MMSE method the criterion of indiscernibility is employed.
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References
Albrecht, V. (1984) On the convergence rate of probability of error in Bayesian discrimination between two Gaussian processes. In: Proc. of the Third Prague Symposium on Asymptotic Statistics, 1983, Elsevier Sci. Publ. B.V., Amsterdam, 165–175.
Albrecht, V. (1985): Estimation of evoked EEG activity by maximum-entropy signal estimator. In: Proc. of IFIP-IMIA Conf. on Medical Decision Making, 1985, North Holland, Amsterdam, 173–176.
Bhansali, R. J., Karavellas, D. (1983): Wiener filtering (with emphasis on frequency-domain approaches). In: Handbook of Statistics 3 — Time series in the frequency domain, 1983, North Holland, Amsterdam, 1–19.
Box, G. E. P., Müller, M. A. (1958): A note on the generation of random normal deviates. Ann. Math. Statist. 29, 610–613.
Gichman, I. I., Skorochod, A. V. (1971): Theory of stochastic processes, Nauka, Moscow (in Russian).
Grenander, U. (1974): Large sample discrimination between two Gaussian processes with different spectra. Ann. Statist. 2, 347–352.
Perez, A. (1973): Asymptotic discernibility of random processes. In: Proc. of the First Prague Symp. on Asymptotic Statistics, 1972, Charles Univ. Press, Prague, 311–322.
Priestley, M. B. (1981): Spectral analysis and time series. Academic Press, London.
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© 1988 Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Albrecht, V. (1988). On Indiscernible Estimators of Stationary Processes. In: Višek, J.Á. (eds) Transactions of the Tenth Prague Conference. Czechoslovak Academy of Sciences, vol 10A-B. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3859-5_13
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DOI: https://doi.org/10.1007/978-94-009-3859-5_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8216-7
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