Principles of Statistical Inference: From a Neo-Fisherian Perspective

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World Scientific, 1997 - Mathematics - 535 pages
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In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term “neo-Fisherian” highlights this.After a unified review of background material (statistical models, likelihood, data and model reduction, first-order asymptotics) and inference in the presence of nuisance parameters (including pseudo-likelihoods), a self-contained introduction is given to exponential families, exponential dispersion models, generalized linear models, and group families. Finally, basic results of higher-order asymptotics are introduced (index notation, asymptotic expansions for statistics and distributions, and major applications to likelihood inference).The emphasis is more on general concepts and methods than on regularity conditions. Many examples are given for specific statistical models. Each chapter is supplemented with problems and bibliographic notes. This volume can serve as a textbook in intermediate-level undergraduate and postgraduate courses in statistical inference.
 

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Contents

STATISTICAL MODELS
1
DATA AND MODEL REDUCTION
33
SURVEY OF SOME BASIC CONCEPTS
71
NUISANCE PARAMETERS
123
EXPONENTIAL FAMILIES
171
EXPONENTIAL DISPERSION FAMILIES
225
GROUP FAMILIES
259
ASYMPTOTIC EXPANSIONS FOR STATISTICS
335
LIKELIHOOD AND HIGHERORDER ASYMPTOTICS
431
A LAWS OF LARGE NUMBERS AND CENTRAL LIMIT
469
B ASYMPTOTIC DISTRIBUTION OF EXTREMES
475
AND FISHERIAN PARADIGMS
483
REFERENCES
489
AUTHOR INDEX
521
SUBJECT INDEX
527
Copyright

ASYMPTOTIC EXPANSIONS FOR DISTRIBUTIONS
381

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