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E-book
Author Barndorff-Nielsen, O. E. (Ole E.)

Title Inference and asymptotics / O.E. Barndorff-Nielsen and D.R. Cox
Published [Place of publication not identified] : Routledge, 2017
Online access available from:
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Description 1 online resource (360 pages)
Series Monographs on statistics and applied probability ; 52
Monographs on statistics and applied probability (Series) ; 52
Contents 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
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
Subject Asymptotic distribution (Probability theory)
Inference.
Mathematical statistics -- Asymptotic theory.
Probabilities.
Asymptotic distribution (Probability theory)
Inference.
Inferência estatística.
Mathematical statistics -- Asymptotic theory.
Probabilities.
Teoria assintótica (inferência estatística)
Form Electronic book
Author Cox, D. R. (David Roxbee)
ISBN 1351438557
9781351438551