Author | Barndorff-Nielsen, Ole E. author |
---|---|
Title | Parametric Statistical Models and Likelihood [electronic resource] / by Ole E. Barndorff-Nielsen |
Imprint | New York, NY : Springer New York, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3934-5 |
Descript | VII, 276 p. online resource |
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. Laplaceโs method. Edgeworth and saddle-point approximations -- 6.1. Laplaceโs 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. Taylorโs formula -- A.2. Fourier transformation -- A.3. Some formulas for matrices and determinants -- A.4. Partially ordered sets, partitions and Mรถbius inversion -- A.5. The Legendre transform -- A.6. A differential geometric inversion result -- References