On Non-Regular Estimation. I. Variance Bounds for Estimators of Location Parameters
作者:
W.R. Blischke,
A.J. Truelove,
P.B. Mundle,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1969)
卷期:
Volume 64,
issue 327
页码: 1056-1072
ISSN:0162-1459
年代: 1969
DOI:10.1080/01621459.1969.10501036
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramér-Rao bound, lead to the trivial resultV(t) ≧0, wheretis any unbiased estimator. A number of alternative bounds for application in the non-regular case have been derived. In this paper previous results of this type are reviewed and an additional bound is given. The specific applications of interest involve estimation of a location parameter. Applications of the bounds to the exponential, uniform and Pearson Type III distributions are investigated.
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