ON THE MONOTONICITY OF A CERTAIN EXPECTATION
成果类型：
Article
署名作者：
KHAN, RA
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348272
发表日期：
1991
页码：
1677-1680
关键词：
摘要：
Let {X(n), n greater-than-or-equal-to 1} be a sequence of random variables and let P-theta be a probability measure under which (X1, ..., X(n)) have joint pdf's f(n)(X1,..., X(n),theta)= L(n)(theta), n greater-than-or-equal-to 1. Suppose u(n) = u(n)(X1,..., X(n)), n greater-than-or-equal-to 1, are statistics such that (u(n) - c)(L(n)(theta') - L(n)(theta)) greater-than-or-equal-to 0, for all inverted A (X1,...,X(n)) n greater-than-or-equal-to 1, for some constant c = c(theta, theta'), theta not-equal theta'. For any increasing function psi and stopping time T, it is shown that E-theta-psi-(u(T)) less-than-or-equal-to E-theta'-psi-(u(T)), provided that one of the expectations is finite and P-theta(T < infinity) = 1. The given result holds for a certain monotone likelihood ratio family and an exponential family in particular. This generalizes a result of Chow and Studden and provides a sequential version of a result of Lehmann.