Order Statistics Estimators of the Location of the Cauchy Distribution
作者:
V.D. Barnett,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1966)
卷期:
Volume 61,
issue 316
页码: 1205-1218
ISSN:0162-1459
年代: 1966
DOI:10.1080/01621459.1966.10482205
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In a recent paper in this Journal, Rothenberg, Fisher and Tilanus [1] discuss a class of estimators of the location parameter of the Cauchy distribution, taking the form of the arithmetic average of a central subset of the sample order statistics. They show that the average of roughly the middle quarter of the ordered sample has minimum asymptotic variance within this class, and that asymptotically it eliminates about 36 per cent of the efficiency loss of the median (the most commonly used estimator) in comparison to the maximum likelihood estimator (m.l.e.). Of course both the m.l.e. and the best linear unbiased estimator based on the order statistics (BLUE) achieve full asymptotic efficiency in the Cramér-Rao sense and there can be no dispute about the relative merits of the three estimators asymptotically, or about the inferiority of the median (with asymptotic efficiency 8/π2ė 0.8 compared with about 0.88 for the estimator of Rothenberg et al.).
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