Contributions to a General Asymptotic Statistical Theory 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 bounds for the power of tests 8.1. Hypotheses and co spaces 8.2. The dimension of the co space 8.3. The concept of asymptotic power functions 8.4. The asymptotic envelope power function 8.5. The power function of asymptotically efficient tests 8.6. Restrictions of the basic family 8.7. Asymptotic envelope power functions using the Hellinger distance 9. Asymptotic bounds for the concentration of estimators 9.1. Comparison of concentrations 9.2. Bounds for asymptotically median unbiased estimators 9.3. Multidimensional functionals 9.4. Locally uniform convergence 9.5. Restrictions of the basic family 9.6. Functionals of induced measures 10. Existence of asymptotically efficient estimators for probability measures 10.1. Asymptotic efficiency 10.2. Density estimators 10.3. Parametric families 10.4. Projections of estimators 10.5. Projections into a parametric family 10.6. Projections into a family of product measures 11. Existence of asymptotically efficient estimators for functionals 11.1. Introduction 11.2. Asymptotically efficient estimators for functionals from asymptotically efficient estimators for probability measures 11.3. Functions of asymptotically efficient estimators are asymptotically efficient 11.4. Improvement of asymptotically inefficient estimators 11.5. A heuristic justification of the improvement procedure 11.6. Estimators with stochastic expansion 12. Existence of asymptotically efficient tests 12.1. Introduction 12.2. An asymptotically efficient critical region 12.3. Hypotheses on functionals 13. Inference for parametric families 13.1. Estimating a functional 13.2. Variance bounds for parametric subfamilies 13.3. Asymptotically efficient estimators for parametric subfamilies 14. Random nuisance parameters 14.1. Introduction 14.2. Estimating a structural parameter in the presence of a known random nuisance parameter 14.3. Estimating a structural parameter in the presence of an unknown random nuisance parameter 15. Inference for symmetric probability measures 15.1. Asymptotic variance bounds for functionals of symmetric distributions 15.2. Asymptotically efficient estimators for functionals of symmetric distributions 15.3. Symmetry in two dimensional distributions 16. Inference for measures on product spaces 16.1. Introduction 16.2. Variance bounds 16.3. Asymptotically efficient estimators for product measures 16.4. Estimators for von Mises functionals 16.5. A special example 17. Dependence — independence 17.1. Measures of dependence 17.2. Estimating measures of dependence 17.3. Tests for independence 18. Two sample problems 18.1. Introduction 18.2. Inherent relationships between x and y 18.3. The tangent spaces 18.4. Testing for equality 18.5. Estimation of a transformation parameter 18.6. Estimation in the proportional failure rate model 18.7. Dependent samples 19. Appendix 19.1. Miscellaneous lemmas 19.2. Asymptotic normality of log likelihood ratios References Notation index Author index.