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020 _a9783030125646
_9978-3-030-12564-6
024 7 _a10.1007/978-3-030-12564-6
_2doi
050 4 _aQ334-342
050 4 _aTA347.A78
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
072 7 _aUYQ
_2thema
082 0 4 _a006.3
_223
100 1 _aRyabko, Daniil.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAsymptotic Nonparametric Statistical Analysis of Stationary Time Series
_h[electronic resource] /
_cby Daniil Ryabko.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aVIII, 77 p. 4 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Computer Science,
_x2191-5776
505 0 _a1 Introduction -- 2 Preliminaries -- 3 Basic inference -- Clustering and change-point problems -- 5 Hypothesis Testing -- 6 Generalizations -- References.
520 _aStationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general qualitative assumptions, such as independence or finite memory, clearly fail. However, it has long been considered too general to be able to make statistical inference. One of the reasons for this is that rates of convergence, even of frequencies to the mean, are not available under this assumption alone. Recently, it has been shown that, while some natural and simple problems, such as homogeneity, are indeed provably impossible to solve if one only assumes that the data is stationary (or stationary ergodic), many others can be solved with rather simple and intuitive algorithms. The latter include clustering and change point estimation among others. In this volume these results are summarize. The emphasis is on asymptotic consistency, since this the strongest property one can obtain assuming stationarity alone. While for most of the problem for which a solution is found this solution is algorithmically realizable, the main objective in this area of research, the objective which is only partially attained, is to understand what is possible and what is not possible to do for stationary time series. The considered problems include homogeneity testing (the so-called two sample problem), clustering with respect to distribution, clustering with respect to independence, change point estimation, identity testing, and the general problem of composite hypotheses testing. For the latter problem, a topological criterion for the existence of a consistent test is presented. In addition, a number of open problems is presented.
650 0 _aArtificial intelligence.
650 0 _aCoding theory.
650 0 _aInformation theory.
650 1 4 _aArtificial Intelligence.
650 2 4 _aCoding and Information Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030125639
776 0 8 _iPrinted edition:
_z9783030125653
830 0 _aSpringerBriefs in Computer Science,
_x2191-5776
856 4 0 _uhttps://doi.org/10.1007/978-3-030-12564-6
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c174972
_d174972