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Principles of statistical inference

Author: D R Cox
Publisher: Cambridge ; New York : Cambridge University Press, 2006.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
In this definitive book, D.R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: D R Cox
ISBN: 0521685672 9780521685672 0521866731 9780521866736
OCLC Number: 70875021
Description: xv, 219 pages : illustrations ; 23 cm
Contents: List of examples --
Preface --
1. Preliminaries --
Summary --
1.1. Starting point --
1.2. Role of formal theory of inference --
1.3. Some simple models --
1.4. Formulation of objectives --
1.5. Two broad approaches to statistical inference --
1.6. Some further discussion --
1.7. Parameters --
Notes 1 --
2. Some concepts and simple applications --
Summary --
2.1. Likelihood --
2.2. sufficiency --
2.3. Exponential family --
3.4. Choice of priors for exponential family problems --
2.5. Simple frequentist discussion --
2.6. Pivots --
Notes 2 --
3. Significance tests --
Summary --
3.1. General remarks --
3.2. Simple significance test --
3.3. One- and two-sided tests --
3.4. Relation with acceptance and rejection --
3.5. Formulation of alternatives and test statistics --
3.6. Relation with interval estimation --
3.7. Interpretation of significance tests --
3.8. Bayesian testing --
Notes 3. 4. More complicated situations --
Summary --
4.1. General remarks --
4.2. General Bayesian formulation --
4.3. Frequentist analysis --
4.4. Some more general frequentist developments --
4.5. Some further Bayesian examples --
Notes 4 --
5. Interpretations of uncertainty --
Summary --
5.1. General remarks --
5.2. Broad roles of probability--
5.3. Frequentist interpretation of upper limits --
5.4. Neyman-Pearson operational criteria --
5.5. Some general aspects of the frequentist approach --
5.6. Yet more on the frequentist approach --
5.7. Personalistic probability --
5.8. Impersonal degree of belief --
5.9. Reference priors --
5.10. Temporal coherency --
5.11. Degree of belief and frequency --
5.12. Statistical implementation of Bayesian analysis --
5.13. Model uncertainty --
5.14. Consistency of data and prior --
5.15. Relevance of frequentist assessment --
1.16. Sequential stopping --
5.17. A simple classification problem --
Notes 5 --
6. Asymptotic theory --
Summary --
6.1. General remarks --
6.2. Scalar parameter --
6.3. Multidimensional parameter --
6.4. Nuisance parameters --
6.5. Tests and model reduction --
6.6. Comparative discussion --
6.7. Profile likelihood as an information summarizer --
6.8. Constrained estimation --
6.9. Semi-asymptotic arguments --
6.10. Numerical-analytic aspects --
6.11. Higher-order asymptotics --
Notes 6. 7. Further aspects of maximum likelihood --
Summary --
7.1. Multimodal likelihoods --
7.2. Irregular form --
7.3. Singular information matrix --
7.4. Failure of model --
7.5. Unusual parameter space --
7.6. Modified likelihoods --
Notes 7 --
8. Additional objectives --
Summary --
8.1. Prediction --
8.2. Decision analysis --
8.3. Point estimation --
8.4. Non-likelihood-based methods --
Notes 8 --
9. Randomization-based analysis --
Summary --
9.1. General remarks --
9.2. Sampling a finite population --
9.3. Design of experiments --
Notes 9 --
Appendix A : A brief history--
Appendix B : A personal view --
References --
Author index --
Subject index.
Responsibility: D.R. Cox.
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Abstract:

No one is better placed than D. R. Cox to give the comprehensive, balanced account of the theory of statistical inference, its main ideas and controversies, that is now needed. This book is for every  Read more...

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'A deep and beautifully elegant overview of statistical inference, from one of the towering figures who created modern statistics. This book should be essential reading for all who call themselves Read more...

 
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