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## Details

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, identity testing, and the general problem of composite hypotheses testing.
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