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Nonparametric Statistical Inference for Ergodic Processes

Daniil Ryabko 1, * Boris Ryabko 2, 3
* Corresponding author
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
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.
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Submitted on : Saturday, March 24, 2012 - 3:57:03 PM
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  • HAL Id : inria-00269249, version 4
  • ARXIV : 0804.0510



Daniil Ryabko, Boris Ryabko. Nonparametric Statistical Inference for Ergodic Processes. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2010, 56 (3), pp.1430-1435. ⟨inria-00269249v4⟩



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