Geodesic
A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 347-351

Voir la notice de l'article provenant de la source Cambridge

DOI

In his paper "Necessary and sufficient statistics for a family of probability distributions", Dynkin (1951) establishes the important concept of rank for such a family with this conclusion: "If the rank is infinite, then the family has no non-trivial sufficient statistic in any size of sample." His concept of rank is based on a theorem, Theorem 2 described below, which has been pointed out by Brown (1964) to be invalid under its hypotheses. This note shows that Dynkin's Theorem 2 remains valid under its original hypotheses provided that the set (in Dynkin's notation) Δ - S is countable. 
Tan, Peter. A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 347-351. doi: 10.4153/CMB-1969-046-5
@article{10_4153_CMB_1969_046_5,
     author = {Tan, Peter},
     title = {A {Note} on a {Theorem} of {Dynkin} on {Necessary} and {Sufficient} {Statistics}},
     journal = {Canadian mathematical bulletin},
     pages = {347--351},
     year = {1969},
     volume = {12},
     number = {3},
     doi = {10.4153/CMB-1969-046-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-046-5/}
}
TY  - JOUR
AU  - Tan, Peter
TI  - A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics
JO  - Canadian mathematical bulletin
PY  - 1969
SP  - 347
EP  - 351
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-046-5/
DO  - 10.4153/CMB-1969-046-5
ID  - 10_4153_CMB_1969_046_5
ER  - 
%0 Journal Article
%A Tan, Peter
%T A Note on a Theorem of Dynkin on Necessary and Sufficient Statistics
%J Canadian mathematical bulletin
%D 1969
%P 347-351
%V 12
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-046-5/
%R 10.4153/CMB-1969-046-5
%F 10_4153_CMB_1969_046_5

Cité par Sources :