Nonparametric statistical inference for ergodic processes

Authors:
Daniil Ryabko;Boris Ryabko
Affiliations:
SequeL, INRIA-Lille Nord Europe, Parc Scientifique de la Haute Borne, Villeneuve d'Ascq, France;Institute of Computational Technologies of Siberian, Branch of Russian Academy of Science, Siberian State University of Telecommunications and Informatics, Novosibirsk, Russia
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

In this work, a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, three problems are considered: goodness-of-fit (or identity) testing, process classification, and the change point problem. For each of the problems a test is constructed that is asymptotically accurate for the case when the data is generated by stationary ergodic processes. The tests are based on empirical estimates of distributional distance.