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27
1 Nonparametric Statistical Inference for Ergodic Processes
"... 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: goo ..."
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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: goodnessoffit (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. Index Terms—Nonparametric hypothesis testing, stationary ergodic processes, goodnessoffit test, process classification, change point problem. I.
Discrimination between Bprocesses is impossible.
"... Two series of binary observations x1, x1,... and y1, y2,... are presented: xn and yn are given at each time n ∈ N. It is assumed that the sequences are generated independently of each other by two Bprocesses. The question of interest is whether the sequences represent a typical realization of two d ..."
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Cited by 19 (17 self)
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Two series of binary observations x1, x1,... and y1, y2,... are presented: xn and yn are given at each time n ∈ N. It is assumed that the sequences are generated independently of each other by two Bprocesses. The question of interest is whether the sequences represent a typical realization of two different processes or of the same one. It is demonstrated that this is impossible to decide, in the sense that every discrimination procedure is bound to err with nonnegligible frequency when presented with sequences from some Bprocesses. This contrasts earlier positive results on Bprocesses, in particular those showing that there are consistent ¯ ddistance estimates for this class of processes, and on ergodic processes, in particular, those establishing consistent change point estimates. Keywords: Process discrimination, Bprocesses, stationary ergodic processes, time series, homogeneity testing 1
Testing composite hypotheses about discretevalued stationary processes
 In ITW : 291– 295
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On hypotheses testing for ergodic processes
 In Proceedgings of Information Theory Workshop (2008
, 1998
"... We propose a method for statistical analysis of time series, that allows us to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, we consider three problems: goodnessoffit (or identity ..."
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Cited by 18 (18 self)
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We propose a method for statistical analysis of time series, that allows us to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary ergodic. Namely, we consider three problems: goodnessoffit (or identity) testing, process classification, and the change point problem. For each of the problems we construct a test 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.
An impossibility result for process discrimination
 In Proceedings of IEEE International Symposium on Information Theory (ISIT’09
, 2009
"... Two series of binary observations x1, x1,... and y1, y2,... are presented: at each time n ∈ N we are given xn and yn. It is assumed that the sequences are generated independently of each other by two stochastic processes. We are interested in the question of whether the sequences represent a typical ..."
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Cited by 9 (8 self)
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Two series of binary observations x1, x1,... and y1, y2,... are presented: at each time n ∈ N we are given xn and yn. It is assumed that the sequences are generated independently of each other by two stochastic processes. We are interested in the question of whether the sequences represent a typical realization of two different processes or of the same one. We demonstrate that this is impossible to decide in the case when the processes are Bprocesses. It follows that discrimination is impossible for the set of all (finitevalued) stationary ergodic processes in general. This result means that every discrimination procedure is bound to err with nonnegligible frequency when presented with sequences from some of such processes. It contrasts earlier positive results on Bprocesses, in particular those showing that there are consistent ¯ ddistance estimates for this class of processes. Keywords: Process discrimination, Bprocesses, stationary ergodic processes, time series, homogeneity testing 1
Article HydroZIP: How Hydrological Knowledge can Be Used to Improve Compression of Hydrological Data
, 2013
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Applications of Universal Source Coding to Statistical Analysis of Time Series
"... We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a stationary and ergodic source asymptotically to the Shannon entropy, ..."
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Cited by 2 (1 self)
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We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a stationary and ergodic source asymptotically to the Shannon entropy, which, in turn, is the best achievable ratio for lossless data compressors. We consider finitealphabet and realvalued time series and the following problems: estimation of the limiting probabilities for finitealphabet time series and estimation of the density for realvalued time series, the online prediction, regression, classification (or problems with side information) for both types of the time series and the following problems of hypothesis testing: goodnessoffit testing, or identity testing, and testing of serial independence. It is important to note that all problems are considered in the framework of classical mathematical statistics and, on the other hand, everyday methods of data compression (or archivers) can be used as a tool for the estimation and testing. It turns out, that quite often the suggested methods and tests are more powerful
Uniform hypothesis testing for finitevalued stationary processes
, 2012
"... Given a discretevalued sample X1,...,Xn, we wish to decide whether it was generated by a distribution belonging to a family H0, or it was generated by a distribution belonging to a family H1. In this work, we assume that all distributions are stationary ergodic, and do not make any further assumpti ..."
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Given a discretevalued sample X1,...,Xn, we wish to decide whether it was generated by a distribution belonging to a family H0, or it was generated by a distribution belonging to a family H1. In this work, we assume that all distributions are stationary ergodic, and do not make any further assumptions (e.g. no independence or mixing rate assumptions). We would like to have a test whose probability of error (both Types I and II) is uniformly bounded. More precisely, we require that for each ε there exists a sample size n such that probability of error is upperbounded by ε for samples longer than n. We find some necessary and some sufficient conditions onH0 andH1 under which a consistent test (with this notion of consistency) exists. These conditions are topological, with respect to the topology of distributional distance.
Zh.: Estimate of complexity of behavioral patterns in ants: analysis of hunting behavior in myrmica rubra (hymenoptera, formicidae) as an example
 Entomol. Rev
, 2011
"... AbstractA method for estimating the complexity of behavioral patterns of ants based on the Kolmogorov complexity is considered. Behavioral sequences are presented as "texts" compressed with the KGB Archiver (v. 1.2). The elements of behavior (a total of 10) singled out from video records ..."
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AbstractA method for estimating the complexity of behavioral patterns of ants based on the Kolmogorov complexity is considered. Behavioral sequences are presented as "texts" compressed with the KGB Archiver (v. 1.2). The elements of behavior (a total of 10) singled out from video records served as an alphabet. The comparison of "successful" and "incomplete" hunting behaviors in Myrmica rubra showed that successful hunting patterns were characterized by less complexity than "incomplete" ones. It was assumed that complete patterns had less redundancy and better predictability. The smallest complexity was revealed in complete hunting patterns of naive (laboratory reared) ants in comparison with members of a natural colony. In perspective, quantitative evaluation of complexity of behavioral patterns will help to evaluate the level of discrete variability within ant colonies.