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Asymptotic nonparametric statistical analysis of stationary time series

Author: Daniil Ryabko
Publisher: Cham, Switzerland : Springer, 2019.
Series: SpringerBriefs in computer science
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ryabko, Daniil.
Asymptotic nonparametric statistical analysis of stationary time series.
Cham, Switzerland : Springer, 2019
(OCoLC)1081000378
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Daniil Ryabko
ISBN: 9783030125646 3030125645 9783030125653 3030125653
OCLC Number: 1089804008
Description: 1 online resource (viii, 77 pages) : illustrations
Contents: Intro; Preface; Contents; 1 Introduction; 1.1 Stationarity, Ergodicity, AMS; 1.2 What Is Possible and What Is Not Possible to Infer from Stationary Processes; 1.3 Overview of the Inference Problems Covered; 2 Preliminaries; 2.1 Stationarity, Ergodicity; 2.2 Distributional Distance; 3 Basic Inference; 3.1 Estimating the Distance Between Processes and Reconstructing a Process; 3.2 Calculating; 3.3 The Three-Sample Problem; 3.4 Impossibility of Discrimination; 3.4.1 Setup and Definitions; 3.4.2 The Main Result; 4 Clustering and Change-Point Problems; 4.1 Time-Series Clustering 4.1.1 Problem Formulation4.1.2 A Clustering Algorithm and Its Consistency; 4.1.3 Extensions: Unknown k, Online Clustering and Clustering with Respect to Independence; 4.1.3.1 Unknown Number of Clusters; 4.1.3.2 Online Clustering; 4.1.3.3 Clustering with Respect to Independence; 4.2 Change-Point Problems; 4.2.1 Single Change Point; 4.2.2 Multiple Change Points, Known Number of Change Points; 4.2.3 Unknown Number of Change Points; 4.2.3.1 Listing Change Points; 4.2.3.2 Known Number of Distributions, Unknown Number of Change Points; 5 Hypothesis Testing; 5.1 Introduction 5.1.1 Motivation and Examples5.2 Types of Consistency; 5.2.1 Uniform Consistency; 5.2.2 Asymmetric Consistency; 5.2.3 Asymptotic Consistency; 5.2.4 Other Notions of Consistency; 5.3 One Example That Explains Hypotheses Testing; 5.3.1 Bernoulli i.i.d. Processes; 5.3.2 Markov Chains; 5.3.3 Stationary Ergodic Processes; 5.4 Topological Characterizations; 5.4.1 Uniform Testing; 5.4.2 Asymmetric Testing; 5.5 Proofs; 5.6 Examples; 5.6.1 Simple Hypotheses, Identity or Goodness-of-Fit Testing; 5.6.2 Markov and Hidden Markov Processes:Bounding the Order; 5.6.3 Smooth Parametric Families 5.6.4 Homogeneity Testing or Process Discrimination5.6.5 Independence; 5.7 Open Problems; 5.7.1 Relating the Notions of Consistency; 5.7.2 Characterizing Hypotheses for WhichConsistent Tests Exist; 5.7.3 Independence Testing; 6 Generalizations; 6.1 Other Distances; 6.1.1 sum Distances; 6.1.2 Telescope Distance; 6.1.3 sup Distances; 6.1.4 Non-metric Distances; 6.1.5 AMS Distributions; 6.2 Piece-Wise Stationary Processes; 6.3 Beyond Time Series; 6.3.1 Processes Over Multiple Dimensions; 6.3.2 Infinite Random Graphs; References
Series Title: SpringerBriefs in computer science
Responsibility: Daniil Ryabko.

Abstract:

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,  Read more...

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