Steffen Lauritzen

Fundamentals of Mathematical Statistics (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This books is meant for a standard one-semester advanced undergraduate or graduate level course on Mathematical Statistics. It covers all the key topics - statistical models, linear normal models, exponential families, estimation, asymptotics of maximum likelihood, significance testing, and models for tables of counts.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 258
• Erscheinungstermin: 17. April 2023
• Englisch
• ISBN-13: 9781000831986
• Artikelnr.: 67695000

Autorenporträt

Steffen Lauritzen is Emeritus Professor of Statistics at the University of Copenhagen and the University of Oxford as well as Honorary Professor at Aalborg University. He is most well known for his work on graphical models, in particular represented in a monograph from 1996 with that title, but he has published in a wide range of topics. He has received numerous awards and honours, including the Guy Medal in Silver from the Royal Statistical Society, where he also is an Honorary Fellow. He was elected to the Royal Danish Academy of Sciences and Letters in 2008 and became a Fellow of the Royal Society in 2011.

Inhaltsangabe

1. Statistical Models. 1.1. Models and parametrizations. 1.2. Likelihood,
score, and information. 1.3. Exercises. 2. Linear Normal Models. 2.1. The
multivariate normal distribution. 2.2. The normal distribution on a vector
space. 2.3. The linear normal model. 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. 3.5. 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. 4.3. The method of
maximum likelihood. 4.4. Exercises. 5. Asymptotic Theory. 5.1. Asymptotic
consistency and normality. 5.2. Asymptotics of moment estimators. 5.3.
Asymptotics in regular exponential families. 5.4. Asymptotics in curved
exponential families. 5.5. More about asymptotics. 5.6. Exercises. 6. Set
Estimation. 6.1. Basic issues and definition. 6.2. Exact confidence regions
by pivots. 6.3. Likelihood based regions. 6.4. Confidence regions by
asymptotic pivots. 6.5. Properties of set estimators. 6.6. Credibility
regions. 6.7. Exercises. 7. Significance Testing. 7.1. The problem. 7.2.
Hypotheses and test statistics. 7.3. Significance and p-values. 7.4.
Critical regions, power, and error types. 7.5. Set estimation and testing.
7.6. Test in linear normal models. 7.7. Determining p-values. 7.8.
Exercises. 8. Models for Tables of Counts. 8.1. Multinomial exponential
families. 8.2. Genetic equilibrium models. 8.3. Contingency tables. 8.4.
Exercises.