Statistical Decision Theory

- Statistical models

- Tests in models with monotonicity properties

- Statistical decision theory

- Comparison of models, reduction by sufficiency

- Invariant statistical decision models

- Large sample approximations of models and decisions

- Estimation

- Testing

- Selection

From the reviews:

"The central theme of this book is 'what optimal decisions are in general and in specific decision problems, and how to derive them'; optimality is understood in terms of the expected loss, i.e. the risk functional, or some function of it.... This monograph is, undoubtedly, a significant event in the development of statistical decision theory." (Yurij S. Kharin, American Mathematical Society, Mathematical Reviews on the Web, MR2421720)

"This book is unique in offering a fuller point of view of selection rules,.... An other feature is that is combines innovation and tradition. This monograph uniquely synthesizes otherwise disparate materials, while establishing connections between classical and modern decision theory. Actually it creates a bridge between the classical results of mathematical statistics and the modern asymptotic decision theory.... also provides a broad coverage of both the frequentist and the Bayes approaches in decision theory." (2009 European Mathematical Society, FIZ Karlsruhe & Springer-Velag, ZBl 1154.62008)

"The central theme of this book is the nature of optimal decisions, in both general and specific problems, and how to reach them. ... This is a deep theoretical and mathematical presentation of decision theory, which I imagine will become a leading reference work for researchers in the area." (David J. Hand, International Statistical Review, Vol. 76 (3), 2008)

"This monograph is written not only as a basis for graduate courses, but also as a reference tool. Readers should be familiar with basic concepts of probability theory, mathematical statistics, and analysis. ... This book also provides a broad coverage of both the frequentist and the Bayes approaches in decision theory. The Bayes approach is considered to be a useful decision-theoretic framework among others, and it is used heavily throughout the book ... ." (R. Schlittgen, Zentralblatt MATH, Vol. 1154, 2009)

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