High-order Vector Markov Chain with Partial Connections in Data Analysis
AbstractA new mathematical model for discrete time series is proposed: homogenous vector Markov chain of the order s with partial connections. Conditional probability distribution
for this model is determined only by a few components of previous vector states. Probabilistic properties of the model are given: ergodicity conditions and conditions
under which the stationary probability distribution is uniform. Consistent statistical estimators for model parameters are constructed.
Bonacich P (2003). Asymptotics of a Matrix Valued Markov Chain Arising in Sociology. Stochastic Processes and their Applications, 104(1), 155-171.
Borovkov A (1998). Mathematical Statistics. Gordon and Breach, New York.
Csiszar I, Shields P (1999). Consistency of the BIC Order Estimator. Electronic research announcements of the American mathematical society, 5, 123-127.
Doob J (1953). Stochastic Processes. Wiley, New York.
Kemeny J, Snell J (1963). Finite Markov Chains. D. Van Nostrand Company, Princeton NJ.
Kharin A (2016). Performance and Robustness Evaluation in Sequential Hypotheses Testing. Communications in Statistics - Theory and Methods, 45(6), 1693-1709.
Kharin A, Kishylau D (2015). Robust Sequential Test for Hypotheses about Discrete Distributions in the Presence of "Outliers". Journal of Mathematical Sciences, 205(1), 68-73.
Kharin A, Shlyk P (2009). Robust Multivariate Bayesian Forecasting under Functional Distortions in the ξ2-metric. Journal of Statistical Planning and Inference, 139(11), 3842-3846.
Kharin Y (1997). Robustness of Clustering under Outliers. Lecture Notes in Computer Science, 1280, 501-512.
Kharin Y (2012). Parsimonious Models for High-order Markov Chains and Their Statistical Analysis. VIII World Congress on Probability and Statistics, pp. 168-169.
Kharin Y, Maltsew M (2011). Algorithms for Statistical Analysis of Markov Chain with Conditional Memory Depth. Informatics, 1, 34-43 (in Russian).
Kharin Y, Petlitskii A (2007). A Markov Chain of Order s with r Partial Connections and Statistical Inference on Its Parameters. Discrete Mathematics and Applications, 17(3), 295-317.
Kharin Y, Zhuk E (1998). Filtering of Multivariate Samples Containing "Outliers" for Clustering. Pattern Recognition Letters, 19(11), 1077-1085.
Voloshko V, Medved E, Kharin Y (2016). Multiresolution Statistical Analysis of DNA. Proceedings of the 13th international conference, pp. 178-181.
Waterman M (1999). Mathematical Methods for DNA Sequences. Chapman and Hall/CRC, Boca Raton, Florida.
How to Cite
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.