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**Statistical models based on counting processes.**
*(English)*
Zbl 0769.62061

Springer Series in Statistics. New York: Springer-Verlag. xi, 767 p. (1993).

This is the book on statistical analysis of event history data. The authors combine both the theoretical and practical aspects of this field of statistics in a lucid way. They give a thorough survey on statistical models based on counting processes. First they introduce the mathematical background, which contains counting processes, compensators, stochastic integration and product integration. They continue by introducing statistical models and nonparametric estimation by treating the Nelson- Aalen estimator, the Kaplan-Meier estimator and the estimator for the transition matrix of a Markov process. They continue by nonparametric hypothesis testing.

Next they introduce parametric models and regression models, which include various generalizations of the Cox model. Then they study the asymptotic efficiency of estimators and tests. The book ends with two new topics in this field of statistics: frailty models and multivariate time scales.

The book contains nineteen datasets, which are repeatedly used to illustrate the use of various statistical methods presented in the book. Each chapter ends with a valuable section containing bibliographic remarks.

Next they introduce parametric models and regression models, which include various generalizations of the Cox model. Then they study the asymptotic efficiency of estimators and tests. The book ends with two new topics in this field of statistics: frailty models and multivariate time scales.

The book contains nineteen datasets, which are repeatedly used to illustrate the use of various statistical methods presented in the book. Each chapter ends with a valuable section containing bibliographic remarks.

Reviewer: E.Valkeila (Helsinki)

### MSC:

62M02 | Markov processes: hypothesis testing |

62M05 | Markov processes: estimation; hidden Markov models |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62M99 | Inference from stochastic processes |