作者: Ole E. Barndorff-Nielsen
DOI:
关键词: Invariant (physics) 、 Mathematics 、 Legendre transformation 、 Pure mathematics 、 Combinatorics 、 Parametric statistics 、 Hermite polynomials 、 Differential geometry 、 Estimating equations 、 Covariant transformation 、 Mathematical statistics
摘要: 0. Introduction.- 0.1. Outline of contents.- 0.2. A few preliminaries.- 1. Likelihood and auxiliary statistics.- 1.1. Likelihood.- 1.2. Moments cumulants log likelihood derivatives.- 1.3. Parametrization invariance.- 1.4. Marginal conditional likelihood.- 1.5. Combinants, auxiliaries, the p*-model.- 1.6. Orthogonal parameters.- 1.7. Pseudo likelihood, profile modified 1.8. Ancillarity conditionality.- 1.9. Partial sufficiency partial ancillarity.- 1.10. expansions.- 1.11. Additional bibliographical notes.- 2. Transformation models exponential models.- 2.1. Group actions invariant measures.- 2.2. 2.3. submodels.- 2.4. Exponential 2.5. transformation 2.6. 3. Reparametrizations differential geometry.- 3.1. Multiarrays.- 3.2. Tensors affine connections.- 3.3. Strings.- 3.4. Covariant differentiation strings.- 3.5. Intertwining.- 3.6. Submanifolds.- 3.7. Geometric 3.8. Manifolds with a Lie group action.- 3.9. Fibre bundles, connections (parallel) transport.- 3.10. 4. Inferential geometric structures.- 4.1. Ancillary statistics conditionality 4.2. Conditionality structures for 4.3. Construction approximately ancillary 4.4. Jacobians 4.5. Geometry parametric 4.6. 5. Cumulants.- 5.1. Elemental properties cumulants.- 5.2. Relations between moments 5.3. An alternative definition generalized 5.4. 6. Laplace's method. Edgeworth saddle-point approximations.- 6.1. method.- 6.2. Hermite polynomials.- 6.3. 6.4. Saddle-point 6.5. 7. Distributions quantities.- 7.1. The distribution maximum estimator.- 7.2. Expansion p*.- 7.3. score vector.- 7.4. ratio 7.5. Modified 7.6. Appendices.- A.1. Taylor's formula.- A.2. Fourier transformation.- A.3. Some formulas matrices determinants.- A.4. Partially ordered sets, partitions Mobius inversion.- A.5. Legendre transform.- A.6. inversion result.- References.