Combinations of Unbiased Estimators of the Mean Which Consider Inequality of Unknown Variances
作者:
J.S. Mehta,
John Gurland,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1969)
卷期:
Volume 64,
issue 327
页码: 1042-1055
ISSN:0162-1459
年代: 1969
DOI:10.1080/01621459.1969.10501035
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The problem considered in this paper is how to combine estimators of the common mean from two samples corresponding to normal populations with different unknown variances. Attention is confined to the case where it is known that the variance of one specific population exceeds that of the other. Three classes of unbiased estimators are presented, one of which is based on a preliminary test of significance regarding the ratio of the population variances. The gain achieved by utilizing the knowledge that the ratio of variances exceeds one is investigated by comparing the efficiencies of these estimators with an estimator presented by Graybill and Deal [1] in which no restriction on the ratio of variances is present.
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