Premium
A NOTE ON PREDICTION SUFFICIENCY (ADEQUACY) AND SUFFICIENCY
Author(s) -
Akahira Masafumi,
Takeuchi Kei
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01182.x
Subject(s) - mathematics , homogeneous , markov chain , combinatorics , space (punctuation) , discrete mathematics , statistics , computer science , operating system
Summary Let(X, A) be a measurable space and P a family of probability measures on A. Let B and C be sub s̀‐algebras of A and B 0 a sub s̀‐algebra of B. It is shown that if B 0 is prediction sufficient (adequate) for B with respect to C and P, and Y is sufficient for B 0 v C with respect to P then Y is sufficient for B v C with respect to P; that if P is homogeneous and (B 0 ; B, C) is Markov for P, and B 0 v C is sufficient for B v c with respect to P, then B 0 is sufficient for B with respect to P; and by example that the Markov property is necessary for the latter proposition to hold.