Data-Based Nonparametric Signal Filtration
DOI:
https://doi.org/10.17713/ajs.v40i1&2.193Abstract
The problem of stochastic signal filtration under nonparametric uncertainties is considered. A probabilistic description of the signal process is assumed to be completely unknown. The Bayes estimator can not be constructed in this case. However if the conditional density of the observation process given signal process belongs to conditionally exponential family, the optimal Bayes estimator is a solution to some non-recurrent equation which is explicitly independent upon the signal process distribution. In this case, the Bayes estimator is expressed in terms of conditional distribution of the observation process, which can be approximated by using of the stable nonparametric procedures, adapted to dependent samples. These stable approximations provide the mean square convergence to Bayes estimator. In the stable kernel nonparametric procedures, a crucial step is to select a proper smoothing parameter (bandwidth) and a regularized parameter, which have aconsiderable influence on the quality of signal filtration. The optimal procedures for selecting of these parameters are proposed. These procedures allow to construct the automatic (data-based) signal filtration algorithm.
References
Bowman, A. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrica, 71, 353-360.
Dobrovidov, A. (1983). Nonparametric methods of nonlinear filtering of stationary random sequenses. Automat. and Remote Control, 44, 757-768.
Dobrovidov, A., and Koshkin, G. (1997). Nonparametric Signal Estimation. Moscow: Phizmatlit.
Dobrovidov, A., and Rudko, I. (2010). Bandwidth selection in nonparametric estimator of density derivative by smoothed cross-validation method. Automation and Remote Control, 71, 42-58.
Duong, T., and Hazelton, M. L. (2005). Cross-validation bandwidth matrices for multivariate kernel density estimation. Scandinavian Journal of Statistics, 32, 485-506.
Hall, P., Marron, J., and Park, B. (1992). Smoothed cross-validation. Probability Theory and Related Fields, 92, 1-20.
Park, B., and Marron, J. (1990). Comparison of data-driven bandwidth selectors. Journal of the American Statistical Association, 85, 66-72.
Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scandinavian Journal of Statistics, 9, 65-78.
Vasiliev, V., Dobrovidov, A., and Koshkin, G. (2004). Nonparametric Estimation of Functionals of Stationary Sequences Distributions (in Russian). Moscow: Nauka.
Downloads
Published
How to Cite
Issue
Section
License
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License.
The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.
Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.
Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.