Author | Yamada, Sakutarล. author |
---|---|
Title | Pivotal Measures in Statistical Experiments and Sufficiency [electronic resource] / by Sakutarล Yamada |
Imprint | New York, NY : Springer New York, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2644-4 |
Descript | VIII, 129 p. online resource |
0 Introduction -- 1 Undominated experiments -- 1.1. Majorized experiments and their decomposition -- 1.2. Weakly dominated experiments -- 1.3. Examples -- 1.4. Bibliographical notes -- 2 PSS, pivotal measure and Neyman factorization -- 2.1. PSS and pivotal measure for majorized experiments -- 2.2. Generalizations of the Neyman factorization theorem -- 2.3. Neyman factorization and pivotal measure in the case of weak domination -- 2.4. Dominated case -- 2.5. Bibliographical notes -- 3 Structure of pairwise sufficient subfield and PSS -- 3.1. Discrete experiment case -- 3.2. Majorized experiment case -- 3.3. Burkholder problem of sufficiency and completions -- 3.4. Bibliographical notes -- 4 The Rao-Blackwell theorem and UMVUE -- 4.1. Rao-Blackwell theorem for PSS in weakly dominated experiments -- 4.2. Converse of a theorem of Lehmann and Scheffรฉ -- 4.3. Bibliographical notes -- 5 Common conditional probability for PSS and its applications -- 5.1. Deficiency -- 5.2. Representation of M-space of majorized experiment -- 5.3. Representation of the common conditional probability for PSS by (T)-integral -- 5.4. Application of the extended notion of common conditional probability for PSS subfield -- 5.5. Bibliographical notes -- 6 Structure of pivotal measure -- 6.1. Minimal L-space -- 6.2. Maximal orthogonal system and pivotal measure -- 6.3. Bibliographical notes -- References -- List of symbols