Statistics Based on Dirichlet Processes and Related Topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
Springer Singapore Pte. Limited
2020
|
| Schriftenreihe: | SpringerBriefs in Statistics Ser
|
| Schlagworte: | |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (80 pages) |
| ISBN: | 9789811569753 |
Internformat
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| 100 | 1 | |a Yamato, Hajime |e Verfasser |4 aut | |
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| 505 | 8 | |a Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Dirichlet Process as Prior Distribution in Nonparametric Inference -- 1.2 Normalized Random Measure -- 1.3 Process Neutral to the Right -- References -- 2 Dirichlet Process, Ewens Sampling Formula, and Chinese Restaurant Process -- 2.1 Dirichlet Process and Ewens Sampling Formula -- 2.2 Chinese Restaurant Process -- 2.3 GEM Distribution -- 2.4 Poisson-Dirichlet Distribution -- 2.5 Asymptotic Properties of Statistics Related with ESF -- 2.5.1 Ewens Sampling Formula -- 2.5.2 Donnelly-Tavaré-Griffiths Formula I -- 2.5.3 Donnelly-Tavaré-Griffiths Formula II -- 2.5.4 Number Kn of Distinct Components (1) -- 2.5.5 Number Kn of Distinct Components (2) -- 2.6 Related Topics -- 2.6.1 Patterns of Communication -- 2.6.2 Pitman Sampling Formula (1) -- 2.6.3 Pitman Sampling Formula (2) -- References -- 3 Nonparametric Estimation of Estimable Parameter -- 3.1 Nonparametric Bayes Estimator of Estimable Parameter -- 3.2 Convex Combination of U-Statistics -- 3.2.1 Preliminaries -- 3.2.2 Convex Combination of U-Statistics -- 3.3 Properties of Convex Combination of U-Statistics -- 3.3.1 H-Decomposition -- 3.3.2 Berry-Esseen Bound -- 3.3.3 Asymptotic Distribution for Degenerate Kernel -- 3.3.4 Corrections to Previous Works -- 3.4 Jackknife Statistic of Convex Combination of U-Statistics -- References -- 4 Statistics Related with Ewens Sampling Formula -- 4.1 Discrete Approximation to Distribution of Number of Components -- 4.1.1 Preliminaries -- 4.1.2 Ewens Sampling Formula -- 4.1.3 Applications -- 4.2 GEM Distribution on Positive Integers -- 4.2.1 Distribution of Statistics from GEM Distribution -- 4.2.2 Frequency Distribution of Order Statistics from GEM Distribution (1) -- 4.2.3 Frequency Distribution of Order Statistics from GEM Distribution (2) -- 4.3 Erdős-Turán Law -- 4.3.1 Erdős-Turán Law for ESF. | |
| 505 | 8 | |a 4.3.2 Erdős-Turán Law for ESF with Random Parameter -- References -- Index | |
| 650 | 4 | |a Applied Statistics.. | |
| 650 | 4 | |a Statistical Theory and Methods.. | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Yamato, Hajime |t Statistics Based on Dirichlet Processes and Related Topics |d Singapore : Springer Singapore Pte. Limited,c2020 |z 9789811569746 |
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Datensatz im Suchindex
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| author | Yamato, Hajime |
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| bvnumber | BV048222990 |
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| contents | Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Dirichlet Process as Prior Distribution in Nonparametric Inference -- 1.2 Normalized Random Measure -- 1.3 Process Neutral to the Right -- References -- 2 Dirichlet Process, Ewens Sampling Formula, and Chinese Restaurant Process -- 2.1 Dirichlet Process and Ewens Sampling Formula -- 2.2 Chinese Restaurant Process -- 2.3 GEM Distribution -- 2.4 Poisson-Dirichlet Distribution -- 2.5 Asymptotic Properties of Statistics Related with ESF -- 2.5.1 Ewens Sampling Formula -- 2.5.2 Donnelly-Tavaré-Griffiths Formula I -- 2.5.3 Donnelly-Tavaré-Griffiths Formula II -- 2.5.4 Number Kn of Distinct Components (1) -- 2.5.5 Number Kn of Distinct Components (2) -- 2.6 Related Topics -- 2.6.1 Patterns of Communication -- 2.6.2 Pitman Sampling Formula (1) -- 2.6.3 Pitman Sampling Formula (2) -- References -- 3 Nonparametric Estimation of Estimable Parameter -- 3.1 Nonparametric Bayes Estimator of Estimable Parameter -- 3.2 Convex Combination of U-Statistics -- 3.2.1 Preliminaries -- 3.2.2 Convex Combination of U-Statistics -- 3.3 Properties of Convex Combination of U-Statistics -- 3.3.1 H-Decomposition -- 3.3.2 Berry-Esseen Bound -- 3.3.3 Asymptotic Distribution for Degenerate Kernel -- 3.3.4 Corrections to Previous Works -- 3.4 Jackknife Statistic of Convex Combination of U-Statistics -- References -- 4 Statistics Related with Ewens Sampling Formula -- 4.1 Discrete Approximation to Distribution of Number of Components -- 4.1.1 Preliminaries -- 4.1.2 Ewens Sampling Formula -- 4.1.3 Applications -- 4.2 GEM Distribution on Positive Integers -- 4.2.1 Distribution of Statistics from GEM Distribution -- 4.2.2 Frequency Distribution of Order Statistics from GEM Distribution (1) -- 4.2.3 Frequency Distribution of Order Statistics from GEM Distribution (2) -- 4.3 Erdős-Turán Law -- 4.3.1 Erdős-Turán Law for ESF. 4.3.2 Erdős-Turán Law for ESF with Random Parameter -- References -- Index |
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| dewey-full | 331.257094 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 331 - Labor economics |
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| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| format | Electronic eBook |
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| id | DE-604.BV048222990 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T19:50:37Z |
| indexdate | 2024-07-10T09:32:27Z |
| institution | BVB |
| isbn | 9789811569753 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033603722 |
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| publishDate | 2020 |
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| publisher | Springer Singapore Pte. Limited |
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| spelling | Yamato, Hajime Verfasser aut Statistics Based on Dirichlet Processes and Related Topics Singapore Springer Singapore Pte. Limited 2020 ©2020 1 Online-Ressource (80 pages) txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in Statistics Ser Description based on publisher supplied metadata and other sources Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Dirichlet Process as Prior Distribution in Nonparametric Inference -- 1.2 Normalized Random Measure -- 1.3 Process Neutral to the Right -- References -- 2 Dirichlet Process, Ewens Sampling Formula, and Chinese Restaurant Process -- 2.1 Dirichlet Process and Ewens Sampling Formula -- 2.2 Chinese Restaurant Process -- 2.3 GEM Distribution -- 2.4 Poisson-Dirichlet Distribution -- 2.5 Asymptotic Properties of Statistics Related with ESF -- 2.5.1 Ewens Sampling Formula -- 2.5.2 Donnelly-Tavaré-Griffiths Formula I -- 2.5.3 Donnelly-Tavaré-Griffiths Formula II -- 2.5.4 Number Kn of Distinct Components (1) -- 2.5.5 Number Kn of Distinct Components (2) -- 2.6 Related Topics -- 2.6.1 Patterns of Communication -- 2.6.2 Pitman Sampling Formula (1) -- 2.6.3 Pitman Sampling Formula (2) -- References -- 3 Nonparametric Estimation of Estimable Parameter -- 3.1 Nonparametric Bayes Estimator of Estimable Parameter -- 3.2 Convex Combination of U-Statistics -- 3.2.1 Preliminaries -- 3.2.2 Convex Combination of U-Statistics -- 3.3 Properties of Convex Combination of U-Statistics -- 3.3.1 H-Decomposition -- 3.3.2 Berry-Esseen Bound -- 3.3.3 Asymptotic Distribution for Degenerate Kernel -- 3.3.4 Corrections to Previous Works -- 3.4 Jackknife Statistic of Convex Combination of U-Statistics -- References -- 4 Statistics Related with Ewens Sampling Formula -- 4.1 Discrete Approximation to Distribution of Number of Components -- 4.1.1 Preliminaries -- 4.1.2 Ewens Sampling Formula -- 4.1.3 Applications -- 4.2 GEM Distribution on Positive Integers -- 4.2.1 Distribution of Statistics from GEM Distribution -- 4.2.2 Frequency Distribution of Order Statistics from GEM Distribution (1) -- 4.2.3 Frequency Distribution of Order Statistics from GEM Distribution (2) -- 4.3 Erdős-Turán Law -- 4.3.1 Erdős-Turán Law for ESF. 4.3.2 Erdős-Turán Law for ESF with Random Parameter -- References -- Index Applied Statistics.. Statistical Theory and Methods.. Probability Theory and Stochastic Processes Erscheint auch als Druck-Ausgabe Yamato, Hajime Statistics Based on Dirichlet Processes and Related Topics Singapore : Springer Singapore Pte. Limited,c2020 9789811569746 |
| spellingShingle | Yamato, Hajime Statistics Based on Dirichlet Processes and Related Topics Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Dirichlet Process as Prior Distribution in Nonparametric Inference -- 1.2 Normalized Random Measure -- 1.3 Process Neutral to the Right -- References -- 2 Dirichlet Process, Ewens Sampling Formula, and Chinese Restaurant Process -- 2.1 Dirichlet Process and Ewens Sampling Formula -- 2.2 Chinese Restaurant Process -- 2.3 GEM Distribution -- 2.4 Poisson-Dirichlet Distribution -- 2.5 Asymptotic Properties of Statistics Related with ESF -- 2.5.1 Ewens Sampling Formula -- 2.5.2 Donnelly-Tavaré-Griffiths Formula I -- 2.5.3 Donnelly-Tavaré-Griffiths Formula II -- 2.5.4 Number Kn of Distinct Components (1) -- 2.5.5 Number Kn of Distinct Components (2) -- 2.6 Related Topics -- 2.6.1 Patterns of Communication -- 2.6.2 Pitman Sampling Formula (1) -- 2.6.3 Pitman Sampling Formula (2) -- References -- 3 Nonparametric Estimation of Estimable Parameter -- 3.1 Nonparametric Bayes Estimator of Estimable Parameter -- 3.2 Convex Combination of U-Statistics -- 3.2.1 Preliminaries -- 3.2.2 Convex Combination of U-Statistics -- 3.3 Properties of Convex Combination of U-Statistics -- 3.3.1 H-Decomposition -- 3.3.2 Berry-Esseen Bound -- 3.3.3 Asymptotic Distribution for Degenerate Kernel -- 3.3.4 Corrections to Previous Works -- 3.4 Jackknife Statistic of Convex Combination of U-Statistics -- References -- 4 Statistics Related with Ewens Sampling Formula -- 4.1 Discrete Approximation to Distribution of Number of Components -- 4.1.1 Preliminaries -- 4.1.2 Ewens Sampling Formula -- 4.1.3 Applications -- 4.2 GEM Distribution on Positive Integers -- 4.2.1 Distribution of Statistics from GEM Distribution -- 4.2.2 Frequency Distribution of Order Statistics from GEM Distribution (1) -- 4.2.3 Frequency Distribution of Order Statistics from GEM Distribution (2) -- 4.3 Erdős-Turán Law -- 4.3.1 Erdős-Turán Law for ESF. 4.3.2 Erdős-Turán Law for ESF with Random Parameter -- References -- Index Applied Statistics.. Statistical Theory and Methods.. Probability Theory and Stochastic Processes |
| title | Statistics Based on Dirichlet Processes and Related Topics |
| title_auth | Statistics Based on Dirichlet Processes and Related Topics |
| title_exact_search | Statistics Based on Dirichlet Processes and Related Topics |
| title_exact_search_txtP | Statistics Based on Dirichlet Processes and Related Topics |
| title_full | Statistics Based on Dirichlet Processes and Related Topics |
| title_fullStr | Statistics Based on Dirichlet Processes and Related Topics |
| title_full_unstemmed | Statistics Based on Dirichlet Processes and Related Topics |
| title_short | Statistics Based on Dirichlet Processes and Related Topics |
| title_sort | statistics based on dirichlet processes and related topics |
| topic | Applied Statistics.. Statistical Theory and Methods.. Probability Theory and Stochastic Processes |
| topic_facet | Applied Statistics.. Statistical Theory and Methods.. Probability Theory and Stochastic Processes |
| work_keys_str_mv | AT yamatohajime statisticsbasedondirichletprocessesandrelatedtopics |