Statistical Decision Rules and Optimal Inference

Front Cover
American Mathematical Soc., 1982 - Mathematics - 499 pages
0 Reviews
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Related books

Contents

1 Statistical problems and statistical decisions
1
2 Probability measures and conditional distributions
13
3 Smooth manifolds and their mappings
37
4Category theory and geometry
50
THE FORMAL DECISION PROBLEM
65
6 Markov geometry of families of probability distributions
76
7 Geometry of dominated families of probability distributions
92
8 Invariant information characteristics
113
16 Continuously differentiable families of probability distributions
228
GEOMETRY OF EXPONENT FAMILIES OF PROBABILITY DISTRIBUTIONS In this chapter we develop the theory of exponent families of prob...
245
18 Exponent families of probability distributions
262
19 Natural parametrization of exponent families
279
20 Conjugate parametrizations of an exponent family of probability distributions
290
21 Distributions of values of the directional statistic of an exponent family and related families
303
22 Nonsynunetric Pythagorean geometry of the information deviation
319
23 Charts of an exponent family of probability distributions
334

EQUIVARIANT DIFFERENTIAL GEOMETRY OF A COLLECTION OF PROBABILITY DISTRIBUTIONS
127
10 Project ive geometry of a collection of probability distributions
140
11 Invariant Riemannian metric on a manifold of probability distributions
156
12 Geodesic mean of probability distributions
165
SMOOTH FAMILIES OF PROBABILITY DISTRIBUTIONS AND THE INFORMATION INEQUALITY 13 Finitedimensional approximation of infi...
185
14 Differentiate families of probability distributions
199
15 The information inequality
213
OPTIMAL DECISION RULES IN THE EQUIVARIANT PROBLEM OF POINT ESTIMATION
355
25 Estimation of the unknown density of a probability distribution of observations
370
26 Invariant loss functions in problems of mathematical statistics 1 In the last two sections we considered wellknown examples of statistical point esti...
391
27 Optimal estimators for smooth families of probability distributions
403
28 Quasihomogeneous families of probability distributions
437
Copyright

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information