Measurement error in nonlinear models: a modern perspective. 2nd ed.

*(English)*Zbl 1119.62063
Monographs on Statistics and Applied Probability 105. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-633-1/hbk; 978-1-4200-1013-8/ebook). xxviii, 455 p. (2006).

This monograph is devoted to the analysis strategies for regression problems where predictors are measured with error, i.e., problems known as measurement error modeling. The interest is focused (almost exclusively) on the analysis of nonlinear regression models, defined such as to include generalized linear models, transform-both-sides models, and quasi-likelihood and variance function problems. There are described general ideas and strategies of estimation and inference, rather than specific problems. The authors’ philosophy is that measurement error occurs in many fields, in a variety of guises, being necessary strategies for handling progressively more difficult problems, starting with logistic regression as one of the most important nonlinear measurement error models, continuing with a hard-core nonlinear regression bioassay problem, change point problem, etc.

Since the first 1995 edition of the book, see the review Zbl 0853.62048, numerous research topics flourished in the field of measurement error and exposure uncertainty, reflected consistently and enclosed into this new edition as follows: (a) Bayesian computation via Markov Chain Monte-Carlo techniques; (b) Longitudinal data and mixed models; (c) Semi-parametric and nonparametric regression methods; (d) Covariance measurement error in survival analysis. Several chapters have been added and/or completely rewritten, including the advances in the currently up-to-date results. Consistent Appendices containing background and technical material, i.e., mathematical and computational basic results useful to each enclosed chapter, make the book to be self-contained. The large bibliography and helpful indexes are further qualities of the book profile.

Here are the titles of the 15 chapters: Chapter 1: Introduction; Chapter 2: Important Concepts; Chapter 3: Linear Regression and Alternation; Chapter 4: Regression Calibration; Chapter 5: Simulation Extrapolation; Chapter 6: Instrumental Variables; Chapter 7: Score Function Methods; Chapter 8: Likelihood an Quasilikelihood; Chapter 9: Bayesian Methods; Chapter 10: Hypothesis Testing; Chapter 11: Longitudinal Data and Mixed Models; Chapter 12: Nonparametric Estimation; Chapter 13: Semiparametric Regression; Chapter 14: Survival Data; Chapter 15: Response Variable Errors.

Since the first 1995 edition of the book, see the review Zbl 0853.62048, numerous research topics flourished in the field of measurement error and exposure uncertainty, reflected consistently and enclosed into this new edition as follows: (a) Bayesian computation via Markov Chain Monte-Carlo techniques; (b) Longitudinal data and mixed models; (c) Semi-parametric and nonparametric regression methods; (d) Covariance measurement error in survival analysis. Several chapters have been added and/or completely rewritten, including the advances in the currently up-to-date results. Consistent Appendices containing background and technical material, i.e., mathematical and computational basic results useful to each enclosed chapter, make the book to be self-contained. The large bibliography and helpful indexes are further qualities of the book profile.

Here are the titles of the 15 chapters: Chapter 1: Introduction; Chapter 2: Important Concepts; Chapter 3: Linear Regression and Alternation; Chapter 4: Regression Calibration; Chapter 5: Simulation Extrapolation; Chapter 6: Instrumental Variables; Chapter 7: Score Function Methods; Chapter 8: Likelihood an Quasilikelihood; Chapter 9: Bayesian Methods; Chapter 10: Hypothesis Testing; Chapter 11: Longitudinal Data and Mixed Models; Chapter 12: Nonparametric Estimation; Chapter 13: Semiparametric Regression; Chapter 14: Survival Data; Chapter 15: Response Variable Errors.

Reviewer: Neculai Curteanu (Iaşi)

##### MSC:

62J02 | General nonlinear regression |

62G08 | Nonparametric regression and quantile regression |

62J12 | Generalized linear models (logistic models) |

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

65C60 | Computational problems in statistics (MSC2010) |

62G10 | Nonparametric hypothesis testing |