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Asymptotic nonparametric statistical...

Ryabko, Daniil.

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Asymptotic nonparametric statistical analysis of stationary time series

Record Type:	Electronic resources : Monograph/item
Title/Author:	Asymptotic nonparametric statistical analysis of stationary time series/ by Daniil Ryabko.
Author:	Ryabko, Daniil.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	viii, 77 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Introduction -- 2 Preliminaries -- 3 Basic inference -- Clustering and change-point problems -- 5 Hypothesis Testing -- 6 Generalizations -- References.
Contained By:	Springer Nature eBook
Subject:	Time-series analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-12564-6
ISBN:	9783030125646

Asymptotic nonparametric statistical analysis of stationary time series
Ryabko, Daniil.

Asymptotic nonparametric statistical analysis of stationary time series[electronic resource] /by Daniil Ryabko. - Cham :Springer International Publishing :2019. - viii, 77 p. :ill., digital ;24 cm. - SpringerBriefs in computer science,2191-5768. - SpringerBriefs in computer science..

1 Introduction -- 2 Preliminaries -- 3 Basic inference -- Clustering and change-point problems -- 5 Hypothesis Testing -- 6 Generalizations -- References.

Stationarity 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.

ISBN: 9783030125646

Standard No.: 10.1007/978-3-030-12564-6doiSubjects--Topical Terms:

532530
Time-series analysis.

LC Class. No.: QA280 / .R93 2019

Dewey Class. No.: 519.55

Asymptotic nonparametric statistical analysis of stationary time series
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520 $a Stationarity 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.
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