Non-Parametric Signal Interpolation

Authors

  • Alexandr V. Dobrovidov Russian Academy of Sciences, Moscow, Russia

DOI:

https://doi.org/10.17713/ajs.v37i1.283

Abstract

This paper considers the problem of interpolation (smoothing) of a partially observable Markov random sequence. For the dynamic observation models, an equation for the interpolation of the posterior probability density is derived. The main goal of this paper is to consider the smoothing problem for the case of unknown distributions of an unobservable component of a random Markov sequence. Successful results were obtained for the strongly stationary Markov processes with mixing and for the conditional density belonging to the exponential family of densities. The resulting method is based on the empirical Bayes approach and kernel nonparametric estimation. The equation for the optimal smoothing estimator is derived in the form independent of unknown distributions of an unobservable process. Such form of the equation allows to use the nonparametric estimates for some conditional functionals in the equation given a set of dependent observations. To compare the nonparametric estimators with optimal mean square smoothing estimators in Kalman scheme, simulation results are given.

References

Briers, M., Douset, A., and Maskell, S. (2003). Smoothing algorithms for state-space models. IEEE Transactions on signal processing, 55, 1-21.

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Khazen, E. (1978). Restoration of the component of a multivariate markov process under the observations of other its components. Probl. Control Inform. Theory, 7 (4),

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Liptser, R., and Shiryaev, A. (1977). Statistics of Random Processes I: General Theory (1977). II: Applications (1978) (2nd ed.). New York: Springer-Verlag.

Vasiliev, V., Dobrovidov, A., and Koshkin, G. (2004). Nonparametric Estimation of Functionals of Stationary Sequences Distributions (2nd ed.). Moscow: Nauka (in

Russian).

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Published

2016-04-03

How to Cite

Dobrovidov, A. V. (2016). Non-Parametric Signal Interpolation. Austrian Journal of Statistics, 37(1), 21–29. https://doi.org/10.17713/ajs.v37i1.283

Issue

Vol. 37 No. 1 (2008)

Section

Articles

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