Fundamentals of mathematical statistics:
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- List of Figures -- List of Tables -- 1. Statistical Models -- 1.1. Models and parametrizations -- 1.1.1. Examples of statistical models -- 1.1.2. Reparametrization -- 1.1.3. Parameter functions -- 1.1.4. Nui...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
2023
|
| Schriftenreihe: | Chapman and Hall/CRC Texts in statistical science series
|
| Schlagworte: | |
| Online-Zugang: | FHI01 Volltext |
| Zusammenfassung: | Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- List of Figures -- List of Tables -- 1. Statistical Models -- 1.1. Models and parametrizations -- 1.1.1. Examples of statistical models -- 1.1.2. Reparametrization -- 1.1.3. Parameter functions -- 1.1.4. Nuisance parameters and parameters of interest -- 1.2. Likelihood, score, and information -- 1.2.1. The likelihood function -- 1.2.1.1. Formal definition -- 1.2.1.2. Equivariance of the likelihood function -- 1.2.1.3. Likelihood as a random variable -- 1.2.2. Score and information -- 1.2.3. Reparametrization and repetition -- 1.3. Exercises -- 2. Linear Normal Models -- 2.1. The multivariate normal distribution -- 2.2. The normal distribution on a vector space -- 2.2.1. Random vectors in V -- 2.2.2. Projections with respect to the concentration -- 2.2.3. Derived distributions -- 2.3. The linear normal model -- 2.3.1. Basic structure -- 2.3.2. Likelihood, score, and information -- 2.4. Exercises -- 3. Exponential Families -- 3.1. Regular exponential families -- 3.2. Examples of exponential families -- 3.3. Properties of exponential families -- 3.4. Constructing exponential families -- 3.4.1. Product families -- 3.4.2. Repeated observations -- 3.4.3. Transformations -- 3.4.4. Affine subfamilies -- 3.5. Moments, score, and information -- 3.6. Curved exponential families -- 3.7. Exercises -- 4. Estimation -- 4.1. General concepts and exact properties -- 4.2. Various estimation methods -- 4.2.1. The method of least absolute deviations -- 4.2.2. The method of least squares -- 4.2.3. M-estimators -- 4.2.4. The method of moments -- 4.3. The method of maximum likelihood -- 4.3.1. General considerations -- 4.3.2. Maximum likelihood in regular exponential families -- 4.4. Exercises -- 5. Asymptotic Theory -- 5.1. Asymptotic consistency and normality. |
| Beschreibung: | 1 Online-Ressource (xiii, 244 Seiten) |
| ISBN: | 9781000831962 9781003272359 |
| DOI: | 10.1201/9781003272359 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1201/9781003272359 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| spelling | Lauritzen, Steffen L. 1947- Verfasser (DE-588)143823574 aut Fundamentals of mathematical statistics Steffen Lauritzen, University of Copenhagen, Denmark, University of Oxford, United Kingdom Boca Raton ; London ; New York CRC Press 2023 1 Online-Ressource (xiii, 244 Seiten) txt rdacontent c rdamedia cr rdacarrier Chapman and Hall/CRC Texts in statistical science series Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- List of Figures -- List of Tables -- 1. Statistical Models -- 1.1. Models and parametrizations -- 1.1.1. Examples of statistical models -- 1.1.2. Reparametrization -- 1.1.3. Parameter functions -- 1.1.4. Nuisance parameters and parameters of interest -- 1.2. Likelihood, score, and information -- 1.2.1. The likelihood function -- 1.2.1.1. Formal definition -- 1.2.1.2. Equivariance of the likelihood function -- 1.2.1.3. Likelihood as a random variable -- 1.2.2. Score and information -- 1.2.3. Reparametrization and repetition -- 1.3. Exercises -- 2. Linear Normal Models -- 2.1. The multivariate normal distribution -- 2.2. The normal distribution on a vector space -- 2.2.1. Random vectors in V -- 2.2.2. Projections with respect to the concentration -- 2.2.3. Derived distributions -- 2.3. The linear normal model -- 2.3.1. Basic structure -- 2.3.2. Likelihood, score, and information -- 2.4. Exercises -- 3. Exponential Families -- 3.1. Regular exponential families -- 3.2. Examples of exponential families -- 3.3. Properties of exponential families -- 3.4. Constructing exponential families -- 3.4.1. Product families -- 3.4.2. Repeated observations -- 3.4.3. Transformations -- 3.4.4. Affine subfamilies -- 3.5. Moments, score, and information -- 3.6. Curved exponential families -- 3.7. Exercises -- 4. Estimation -- 4.1. General concepts and exact properties -- 4.2. Various estimation methods -- 4.2.1. The method of least absolute deviations -- 4.2.2. The method of least squares -- 4.2.3. M-estimators -- 4.2.4. The method of moments -- 4.3. The method of maximum likelihood -- 4.3.1. General considerations -- 4.3.2. Maximum likelihood in regular exponential families -- 4.4. Exercises -- 5. Asymptotic Theory -- 5.1. Asymptotic consistency and normality. Mathematical statistics Electronic books Erscheint auch als Druck-Ausgabe Fundamentals of mathematical statistics First edition Boca Raton, FL : C&H/CRC Press, 2023 pages cm 9781032223827 9781032223834 https://doi.org/10.1201/9781003272359 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Lauritzen, Steffen L. 1947- Fundamentals of mathematical statistics |
| title | Fundamentals of mathematical statistics |
| title_auth | Fundamentals of mathematical statistics |
| title_exact_search | Fundamentals of mathematical statistics |
| title_exact_search_txtP | Fundamentals of mathematical statistics |
| title_full | Fundamentals of mathematical statistics Steffen Lauritzen, University of Copenhagen, Denmark, University of Oxford, United Kingdom |
| title_fullStr | Fundamentals of mathematical statistics Steffen Lauritzen, University of Copenhagen, Denmark, University of Oxford, United Kingdom |
| title_full_unstemmed | Fundamentals of mathematical statistics Steffen Lauritzen, University of Copenhagen, Denmark, University of Oxford, United Kingdom |
| title_short | Fundamentals of mathematical statistics |
| title_sort | fundamentals of mathematical statistics |
| url | https://doi.org/10.1201/9781003272359 |
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