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Cramer-Rao type information inequalities for the risks of median-unbiased estimators with respect to arbitrary monotonic loss function

Title
Cramer-Rao type information inequalities for the risks of median-unbiased estimators with respect to arbitrary monotonic loss function
Authors
문보영
Issue Date
1994
Department/Major
대학원 통계학과
Publisher
이화여자대학교 대학원
Degree
Master
Advisors
소병수
Abstract
본 논문에서는 임의의 단조 손실함수 ( monotonic loss function ) 에 관하여, 중간값불편추정량 ( median-unbiased estimator ) 의 risk에 대한 새로운 Cramer-Rao type의 정보한계 ( information bound ) 를 유도하였다. 아울러, 한계값 ( bound ) 에 도달하는 유용한 필요,충분 조건을 찾아서 이들이 단조유도비 ( monotone likelihood ratio ) 성질을 만족하는 분포및 strongly unimodal 성질을 가지는 위치 ( location ) 그리고 척도( scale ) 분포족 ( family ) 에서 성립됨을 보였다.;We derive a class of sharp Cramer-Rao type information bounds for the risks of the median-unbiased estimators with respect to arbitrary monotonic loss functions. We also obtain the necessary and sufficient conditions for the attainability of the information bounds and show that these bounds are attained not only for the family of distributions with monotone likelihood ratio (MLR) property but also for the strongly unimodal location and scale families.
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