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OPTIMAL CRITICAL VALUES FOR A PRELIMINARY TEST IN POOLING MEANS
Author(s) -
Ohtani Kazuhiro,
Toyoda Toshihisa
Publication year - 1979
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1979.tb01130.x
Subject(s) - regret , statistics , mathematics , estimator , pooling , minimax , variance (accounting) , mean squared error , population , econometrics , mathematical optimization , computer science , artificial intelligence , economics , demography , accounting , sociology
Summary Given two random samples from normal populations with the same known variance, the experimenter wishes to estimate the mean of the fist population. Whether to pool the two samples or not is made to depend on the result of a preliminary normal test. The bias and mean square error of the pre‐test estimator are presented. Based on two different criteria, a minimax regret and a minimum expected regret ones, the optimal critical values for the pre‐test are given. The minimax regret value is unique (about 1.37), while the alternative values vary depending on the mean and precision included in the prior distribution.