Statistical Modelling by Exponential Families

ISBN-13: 9781108701112 / Angielski / Miękka / 2019 / 296 str.

Rolf Sundberg (Stockholms Universitet)

Opis

This readable, digestible introduction to exponential families of distributions covers the essential theory and demonstrates its use in applications. Containing a vast set of examples and numerous exercises, it is written for graduate students and researchers with a background in basic statistical inference.

Recenzje

'This book is perfect for an introductory theoretical graduate course but its parts could also definitely be used in a more applied course. The only prerequisite is basic mathematical statistics. The book is also very handy as a general reference on exponential families. To keep the content simple, the author sometimes avoids the most technical details; however, all necessary references are provided for the reader's convenience. In this sense the book can be used by any researcher interested in exponential families from either a more theoretical or more applied point of view.' Piotr Zwiernik, MathSciNet

Spis treści

1. What is an exponential family?; 2. Examples of exponential families; 3. Regularity conditions and basic properties; 4. Asymptotic properties of the MLE; 5. Testing model-reducing hypotheses; 6. Boltzmann's law in statistics; 7. Curved exponential families; 8. Extension to incomplete data; 9. Generalized linear models; 10. Graphical models for conditional independence structures; 11. Exponential family models for social networks; 12. Rasch models for item response and related models; 13. Models for processes in space or time; 14. More modelling exercises; Appendix A. Statistical concepts and principles; Appendix B. Useful mathematics.