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Unbiased estimation of the variance of the Graybill‐Deal estimator of the common mean of several normal populations
Author(s) -
Sinha Bimal Kumar
Publication year - 1985
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315154
Subject(s) - minimum variance unbiased estimator , bias of an estimator , stein's unbiased risk estimate , efficient estimator , mathematics , estimator , statistics , consistent estimator , mean squared error , variance (accounting) , trimmed estimator , truncation (statistics) , estimation , efficiency , econometrics , economics , accounting , management
An identity for the chi‐squared distribution is used to derive an unbiased estimator of the variance of the familiar Graybill‐Deal (1959) estimator of the common mean of several normal populations with possibly different unknown variances. This result appears to be new. It is observed that the unbiased estimator is a convergent series whose suitable truncation allows unbiased estimation up to any desired degree of accuracy.