Exact solutions to the Behrens–Fisher Problem: Asymptotically optimal and finite sample efficient choice among

The problem of testing the equality of two normal means when variances are not known is called the Behrens–Fisher Problem. This problem has three known exact solutions, due, respectively, to Chapman, to Prokof’yev and Shishkin, and to Dudewicz and Ahmed. Each procedure has level alpha and power beta...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2007-05, Vol.137 (5), p.1584-1605
Main Authors: Dudewicz, Edward J., Ma, Yan, Mai, Enping (Shirley), Su, Haiyan
Format: Article
Language:English
Subjects:
Asymptotically optimal tests
Behrens–Fisher Problem
Chapman procedure
Comparisons
Dudewicz–Ahmed procedure
Exact level tests
Exact sciences and technology
Exact solutions
Finite-sample efficiency
General topics
Heteroscedasticity
Linear inference, regression
Mathematics
Probability and statistics
Prokof’yev–Shishkin procedure
Recommendation for practical use
Sciences and techniques of general use
Statistics
Testing equality of means
Tests of hypotheses
Tests with specified power
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Summary:The problem of testing the equality of two normal means when variances are not known is called the Behrens–Fisher Problem. This problem has three known exact solutions, due, respectively, to Chapman, to Prokof’yev and Shishkin, and to Dudewicz and Ahmed. Each procedure has level alpha and power beta when the means differ by a given amount delta, both set by the experimenter. No single-sample statistical procedures can make this guarantee. The most recent of the three procedures, that of Dudewicz and Ahmed, is asymptotically optimal. We review the procedures, and then compare them with respect to both asymptotic efficiency and also (using simulation) in finite samples. Of these exact procedures, based on finite-sample comparisons the Dudewicz–Ahmed procedure is recommended for practical use.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2006.09.007