SOME ORTHOGONALITY PRESERVING KERNELS WHICH ARE NOT COMPLETELY ORTHOGONAL
成果类型：
Article
署名作者：
MAULDIN, RD; VONWEIZSACKER, H
署名单位：
University of Kaiserslautern
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990552
发表日期：
1991
页码：
396-400
关键词：
摘要：
It is shown that a perturbed Bernoulli probability transition kernel yields an explicit example of an orthogonality preserving kernel which is not completely orthogonal. In statistical language, such a kernel defines models P(theta), theta-epsilon [0, 1], in which there is no estimate that estimates theta perfectly for all theta, but there is, for any given prior distribution on theta and hypothesis H0 subset-of [0, 1], a perfect test for H0 against its complement [0, 1] / H0. It is also demonstrated with an analysis and an application of sets and maps with the Baire property that there are continuum many nonisomorphic atomless orthogonality preserving transition kernels which are not completely orthogonal. Our methods may be regarded as refinements of those used by Blackwell.