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Efficient and adaptive estimation for semiparametric models. (English) Zbl 0786.62001
Johns Hopkins Series in the Mathematical Sciences. Baltimore, MD: The Johns Hopkins University Press. xix, 560 p. $ 114.00 (1993).
This book deals with the problem of estimation in situations where some features of the data can be modelled parametrically but no assumptions can be made for other features. The material covered in the book deals with (i) the development of methods of estimation in the context of semiparametric models viewed as natural extensions and developments of the corresponding bounds and methods in the classical parametric models, (ii) applications of the techniques to a broad range of models, (iii) development of the theory of information bounds for estimation of infinite-dimensional parameters and (iv) a coherent heuristic view of the methods of estimation used in semiparametric models. The material is covered in seven chapters together with an appendix. A number of statistical models are discussed in Chapter 1. Chapter 2 deals with asymptotic inference for parametric models. Chapter 3 deals with information bounds for Euclidean parameters in infinite-dimensional models. Chapter 4 provides a classification of interesting parametric models according to common features of their tangent spaces. The theory and methods developed in Chapter 2-3 are extended to the case of general infinite-dimensional parameters in nonparametric and semiparametric models in Chapter 5. Information bounds for infinite-dimensional parameters of some of the models investigated in Chapter 4 are given in Chapter 6. Chapter 7 deals with the construction of estimates. Necessary functional analysis and other material required for reading the book are summarized in the Appendix.
Reviewer: K.Alam (Clemson)

62-02Research monographs (statistics)
62F10Point estimation
62F12Asymptotic properties of parametric estimators
62F35Robustness and adaptive procedures (parametric inference)
62G05Nonparametric estimation
62G35Nonparametric robustness