Parametric Statistical Models and Likelihood

Parametric Statistical Models and Likelihood by Ole E Barndorff-Nielsen.

This book is a slightly revised and expanded version of a set I I I of notes used for a lecture series given at the Ecole dlEte de I Probabilites at st. Flour in August 1986. In view of the statistical nature of the material discussed herein it was agreed to publish the material as a separate volume...

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Bibliographic Details
Main Author: Barndorff-Nielsen, Ole E. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1988.
Edition:1st ed. 1988.
Series:Lecture Notes in Statistics, 50
Springer eBook Collection.
Subjects:
Applied mathematics.
Engineering mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 0. Introduction
  • 0.1. Outline of contents
  • 0.2. A few preliminaries
  • 1. Likelihood and auxiliary statistics
  • 1.1. Likelihood
  • 1.2. Moments and cumulants of log likelihood derivatives
  • 1.3. Parametrization invariance
  • 1.4. Marginal and conditional likelihood
  • 1.5. Combinants, auxiliaries, and the p*-model
  • 1.6. Orthogonal parameters
  • 1.7. Pseudo likelihood, profile likelihood and modified profile likelihood
  • 1.8. Ancillarity and conditionality
  • 1.9. Partial sufficiency and partial ancillarity
  • 1.10. Likelihood expansions
  • 1.11. Additional bibliographical notes
  • 2. Transformation models and exponential models
  • 2.1. Group actions and invariant measures
  • 2.2. Transformation models
  • 2.3. Transformation submodels
  • 2.4. Exponential models
  • 2.5. Exponential transformation models
  • 2.6. Additional bibliographical notes
  • 3. Reparametrizations and differential geometry
  • 3.1. Multiarrays
  • 3.2. Tensors and affine connections
  • 3.3. Strings
  • 3.4. Covariant differentiation and strings
  • 3.5. Intertwining
  • 3.6. Submanifolds
  • 3.7. Geometric measures
  • 3.8. Manifolds with a Lie group action
  • 3.9. Fibre bundles, connections and (parallel) transport
  • 3.10. Additional bibliographical notes
  • 4. Inferential and geometric structures
  • 4.1. Ancillary statistics and conditionality structures
  • 4.2. Conditionality structures for transformation models
  • 4.3. Construction of approximately ancillary statistics
  • 4.4. Jacobians of conditionality structures
  • 4.5. Geometry of parametric models
  • 4.6. Additional bibliographical notes
  • 5. Cumulants
  • 5.1. Elemental properties of cumulants
  • 5.2. Relations between moments and cumulants
  • 5.3. An alternative definition of generalized cumulants
  • 5.4. Additional bibliographical notes
  • 6. Laplace’s method. Edgeworth and saddle-point approximations
  • 6.1. Laplace’s method
  • 6.2. Hermite polynomials
  • 6.3. Edgeworth approximations
  • 6.4. Saddle-point approximations
  • 6.5. Additional bibliographical notes
  • 7. Distributions of likelihood quantities
  • 7.1. The distribution of the maximum likelihood estimator
  • 7.2. Expansion of p*
  • 7.3. The distribution of the score vector
  • 7.4. The distribution of likelihood ratio statistics
  • 7.5. Modified profile likelihood
  • 7.6. Additional bibliographical notes
  • Appendices
  • A.1. Taylor’s formula
  • A.2. Fourier transformation
  • A.3. Some formulas for matrices and determinants
  • A.4. Partially ordered sets, partitions and Möbius inversion
  • A.5. The Legendre transform
  • A.6. A differential geometric inversion result
  • References.

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