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A Sufficient Statistic for Con‐invariant Test Problems
Author(s) -
Schindler Werner
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941690118
Subject(s) - mathematics , statistic , invariant (physics) , test statistic , lie group , test (biology) , construct (python library) , symmetry (geometry) , pure mathematics , statistics , combinatorics , discrete mathematics , statistical hypothesis testing , geometry , mathematical physics , computer science , paleontology , biology , programming language
In this paper we will construct a sufficient statistic for test problems on G × G × … × G where G is a compact connected Lie group and every admissible hypothesis fulfills a particular symmetry condition. An explicit formula for this sufficient statistic will be derived for G = SO( n ) which is the case of most practical interest.