Measurement error in nonlinear models.

*(English)*Zbl 0853.62048
Monographs on Statistics and Applied Probability. 63. London: Chapman & Hall. xxiv, 305 p. (1995).

This monograph provides analysis strategies for regression problems in which predictions are measured with error. These problems lie almost exclusively in the analysis of nonlinear regression models, transform-both-sides models, and quasilikelihood and variance function problems. The book deals with general ideas and strategies of estimation and inference, and not with specific problems.

The book can be divided into four main parts. The first part (chapters 1-2) is introductory. This part gives a number of applications and an overview on ideas from regression. The second part (chapters 3-6) gives the ideas on so-called functional modelling, where the distribution of the true predictor is not modelled parametrically. In addition, it is assumed that the true predictor is never observable. The third part (chapters 7-8) concerns structural modeling, meaning that the distribution of the true predictor is parametrically modeled. The likelihood approach to estimation and Bayesian modeling is described. The fourth part (chapters 9-11) is devoted to functional techniques which are applicable when the predictor can be observed in a subset of the study. A variety of topics like case-control studies, differential measurement error, functional mixture methods and survival analysis are also discussed.

This book will be useful for statisticians and specialists in biometry, epidemiology and ecology.

The book can be divided into four main parts. The first part (chapters 1-2) is introductory. This part gives a number of applications and an overview on ideas from regression. The second part (chapters 3-6) gives the ideas on so-called functional modelling, where the distribution of the true predictor is not modelled parametrically. In addition, it is assumed that the true predictor is never observable. The third part (chapters 7-8) concerns structural modeling, meaning that the distribution of the true predictor is parametrically modeled. The likelihood approach to estimation and Bayesian modeling is described. The fourth part (chapters 9-11) is devoted to functional techniques which are applicable when the predictor can be observed in a subset of the study. A variety of topics like case-control studies, differential measurement error, functional mixture methods and survival analysis are also discussed.

This book will be useful for statisticians and specialists in biometry, epidemiology and ecology.

Reviewer: N.Leonenko (Kiev)

##### MSC:

62J02 | General nonlinear regression |

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

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |