Contributions to a General Asymptotic Statistical Theory [Paperback]

0. Introduction.- 0.1. Why asymptotic theory?.- 0.2. The object of a unified asymptotic theory,.- 0.3. Models,.- 0.4. Functionals,.- 0.5. What are the purposes of this book?.- 0.6. A guide to the contents,.- 0.7. Adaptiveness,.- 0.8. Robustness,.- 0.9. Notations,.- 1. The local structure of families of probability measures.- 1.1. The tangent cone T(P,?),.- 1.2. Properties of T(P,?) - properties of ?,.- 1.3. Convexity of T(P,?),.- 1.4. Symmetry of T(P,?),.- 1.5. Tangent spaces of induced measures,.- 2. Examples of tangent spaces.- 2.1. Full tangent spaces,.- 2.2. Parametric families,.- 2.3. Families of symmetric distributions,.- 2.4. Measures on product spaces,.- 2.5. Random nuisance parameters,.- 2.6. A general model,.- 3. Tangent cones.- 3.1. Introduction,.- 3.2. Order with respect to location,.- 3.3. Order with respect to concentration,.- 3.4. Order with respect to asymmetry,.- 3.5. Monotone failure rates,.- 3.6. Positive dependence,.- 4. Differentiable functionals.- 4.1. The gradient of a functional,.- 4.2. Projections into convex sets,.- 4.3. The canonical gradient,.- 4.4. Multidimensional functionals,.- 4.5. Tangent spaces and gradients under side conditions,.- 4.6. Historical remarks,.- 5. Examples of differentiable functionals.- 5.1. Von Mises functionals,.- 5.2. Minimum contrast functionals,.- 5.3. Parameters,.- 5.4. Quantiles,.- 5.5. A location functional,.- 6. Distance functions for probability measures.- 6.1. Some distance functions,.- 6.2. Asymptotic relations between distance functions,.- 6.3. Distances in parametric families,.- 6.4. Distances for product measures,.- 7. Projections of probability measures.- 7.1. Motivation,.- 7.2. The projection,.- 7.3. Projections defined by distances,.- 7.4. Projections of measures  projections of densities,.- 7.5. Iterated projections,.- 7.6. Projections into a parametric family,.- 7.7. Projections into a family of product measures,.- 7.8. Projections into a family of symmetric distributions,.- 8. Asymptotic boundl3³