Miscugli meno favorevoli
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In the Neyman-Pearson Theory the notion of least favorable mixture provides a reduction of a composite null hypothesis to a simple one that is equivalent for finding a most powerful test against a simple alternative.
The aim of this paper is to prove a property of mixtures from which follows Lehmann-Stein Theorem (1948) connecting least favorable mixtures with most powerful tests.
As application classical χ2 test for the variance of a Normal distribution with unknown mean is considered.
Keywords: Most Powerful Test, Neyman-Pearson Theory, Least Favorable Mixture.
Author biographyPiero Quatto, Dipartimento di Statistica – Università degli Studi di Milano-Bicocca via Bicocca degli Arcimboldi, 8 - 20126 Milano (e-mail: firstname.lastname@example.org).