##
**The EM algorithm and extensions.**
*(English)*
Zbl 0882.62012

Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. New York, NY: John Wiley & Sons. xviii, 274 p. (1997).

This book deals with the Expectation – Maximization algorithm (EM algorithm). This is a type of algorithm for the maximum likelihood estimation in a wide variety of problems when there are incomplete data. Examples of this type of data include the case where there are missing data or the distributions are truncated or censored. The EM algorithm was originally developed by A. P. Dempster, N. M. Laird and D. B. Rubin [J. R. Stat. Soc., Ser. B 39, 1-38 (1977; Zbl 0364.62022)].

This book is aimed at giving an introduction to the principles and the methodology of the EM algorithm and its possible applications. The contents are as follows: Chapter 1: General Introduction; Chapter 2: Examples of the EM Algorithm; Chapter 3: Basic Theory of the EM Algorithm; Chapter 4: Standard Errors and Speeding up Convergence; Chapter 5: Extensions of the EM Algorithm; Chapter 6: Miscellaneous Topics.

The authors have illustrated the theory with a large number of examples and the book is well-written. The material is presented at a level accessible to graduate students in statistics. I strongly recommend this book for all those interested in “Statistical Inference and Data Analysis”. It is a welcome addition to the literature on “Statistical Inference”.

This book is aimed at giving an introduction to the principles and the methodology of the EM algorithm and its possible applications. The contents are as follows: Chapter 1: General Introduction; Chapter 2: Examples of the EM Algorithm; Chapter 3: Basic Theory of the EM Algorithm; Chapter 4: Standard Errors and Speeding up Convergence; Chapter 5: Extensions of the EM Algorithm; Chapter 6: Miscellaneous Topics.

The authors have illustrated the theory with a large number of examples and the book is well-written. The material is presented at a level accessible to graduate students in statistics. I strongly recommend this book for all those interested in “Statistical Inference and Data Analysis”. It is a welcome addition to the literature on “Statistical Inference”.

Reviewer: B.L.S.Prakasa Rao (New Delhi)

### MSC:

62F10 | Point estimation |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62F99 | Parametric inference |

65C99 | Probabilistic methods, stochastic differential equations |