Inference and asymptotics / O.E. Barndorff-Nielsen and D.R. Cox.
Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the origi...
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Full Text (via Taylor & Francis) |
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| Format: | eBook |
| Language: | English |
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[Place of publication not identified] :
Routledge,
2017.
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| Series: | Monographs on statistics and applied probability (Series) ;
52. |
| Subjects: |
MARC
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| 100 | 1 | |a Barndorff-Nielsen, O. E. |q (Ole E.) | |
| 245 | 1 | 0 | |a Inference and asymptotics / |c O.E. Barndorff-Nielsen and D.R. Cox. |
| 264 | 1 | |a [Place of publication not identified] : |b Routledge, |c 2017. | |
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| 490 | 1 | |a Monographs on statistics and applied probability ; |v 52. | |
| 505 | 0 | |a Cover -- Title Page -- Copyright Page -- Table of Contents -- Preface -- 1: Preliminaries -- 1.1 Introduction -- 1.2 Normal theory linear model -- 1.3 Exponential models -- 1.4 Transformation models -- 1.5 Invariance -- Further results and exercises -- Bibliographic notes -- 2: Some general concepts -- 2.1 Introduction -- 2.2 Likelihood -- 2.3 Sufficiency -- 2.4 Conditioning and some general concepts -- 2.5 Ancillarity -- 2.6 Examination of model adequacy -- 2.7 Parameter orthogonality -- 2.8 Review of transformation models -- 2.9 Review of prime exponential models -- 2.10 Review of curved exponential models -- Further results and exercises -- Bibliographic notes -- 3: First-order theory -- 3.1 Introduction -- 3.2 Main statistics: no nuisance parameters -- 3.3 Distribution theory: no nuisance parameters -- 3.4 Profile likelihood -- 3.5 Further statistics: nuisance parameter case -- 3.6 Effects of parameter orthogonality -- 3.7 Distribution theory: nuisance parameter case -- 3.8 Non-standard cases -- Further results and exercises -- Bibliographic notes -- 4: Higher-order theory: preliminaries and motivations -- 4.1 Introduction -- 4.2 Choice between different statistics: qualitative considerations -- 4.3 The reasons for modifying simple likelihood-based methods -- 4.4 Higher-order theory: the key questions -- Further results and exercises -- Bibliographic notes -- 5: Some tools of higher-order theory -- 5.1 Introduction -- 5.2 Log-likelihood derivatives and mixed log model derivatives -- 5.3 Expansion of likelihood quantities: expected/observed case -- 5.4 Expansion of likelihood quantities: observed case -- 5.5 Translation between observed and expected expressions -- 5.6 Yokes and invariant calculations -- 5.7 Appendix: Differentiation of matrix quantities -- Further results and exercises -- Bibliographic notes. | |
| 505 | 8 | |a 6: Higher-order theory: likelihood combinants -- 6.1 Introduction -- 6.2 The p*-formula -- 6.3 The score and the profile score -- 6.4 The maximum likelihood estimator revisited -- 6.5 The likelihood ratio -- 6.6 The directed likelihood -- 6.7 Approximate interval probabilities -- Further results and exercises -- Bibliographic notes -- 7: Higher-order theory: some further results and tools -- 7.1 Introduction -- 7.2 Approximate sufficiency and ancillarity -- 7.3 Jacobians of conditionality structures -- 7.4 Derivation of p† and p* for curved exponential models -- 7.5 The effect of sampling rules -- 7.6 Independence of second order -- Further results and exercises -- Bibliographic notes -- 8: Various notions of pseudo-likelihood and higher-order theory -- 8.1 Introduction -- 8.2 Modified profile likelihood -- 8.3 Stable adjustments of profile likelihood -- 8.4 Stable adjustments of directed likelihood -- 8.5 Large number of nuisance parameters -- 8.6 Further definitions of pseudo-likelihood -- Further results and exercises -- Bibliographic notes -- 9: Further aspects -- 9.1 Pivots -- 9.2 Estimating equations and quasi-likelihood -- 9.3 Stochastic processes and time series -- 9.4 Prediction -- 9.5 Asymptotic randomization theory -- Further results and exercises -- Bibliographic notes -- References -- Author index -- Subject index. | |
| 520 | |a Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory. | ||
| 650 | 0 | |a Asymptotic distribution (Probability theory) | |
| 650 | 0 | |a Inference. | |
| 650 | 0 | |a Mathematical statistics |x Asymptotic theory. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 7 | |a Asymptotic distribution (Probability theory) |2 fast |0 (OCoLC)fst00819866. | |
| 650 | 7 | |a Inference. |2 fast |0 (OCoLC)fst00972355. | |
| 650 | 7 | |a Mathematical statistics |x Asymptotic theory. |2 fast |0 (OCoLC)fst01012128. | |
| 650 | 7 | |a Probabilities. |2 fast |0 (OCoLC)fst01077737. | |
| 700 | 1 | |a Cox, D. R. |q (David Roxbee) | |
| 830 | 0 | |a Monographs on statistics and applied probability (Series) ; |v 52. | |
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