Fundamentals of mathematical statistics
著者
書誌事項
Fundamentals of mathematical statistics
（Texts in statistical science）
C&H/CRC Press, 2023
1st ed.
- :hbk.
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注記
Includes bibliographical references (p.237-238) and index.
内容説明・目次
内容説明
Features:
A concise yet rigorous introduction to a one-semester course on mathematical statistics
Covers all the key topics
Assumes a solid background in mathematics and probability
Numerous examples illustrate the topics
Many exercises enhance understanding of the material and enable course use
目次
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.
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