Exponential families in theory and practice
著者
書誌事項
Exponential families in theory and practice
（Institute of Mathematical Statistics textbooks, 16）
Cambridge University Press, 2023
- : pbk
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注記
Includes bibliographical references (p. 239-241) and index
内容説明・目次
内容説明
During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.
目次
- 1. One-parameter exponential families
- 2. Multiparameter exponential families
- 3. Generalized linear models
- 4. Curved exponential families, eb, missing data, and the em algorithm
- 5. Bootstrap confidence intervals
- Bibliography
- Index.
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