Unbiased tests for some one‐sided testing problems
Author(s) -
Cohen Arthur,
Sackrowitz Harold B.
Publication year - 1990
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 - 10.2307/3315840
Subject(s) - mathematics , statistics , homogeneity (statistics) , combinatorics , normality , exponential family , population , demography , sociology
Abstract Unbiased tests are found for various testing problems. In the first model considered we test homogeneity of k + 1 independent one‐parameter exponential family populations vs. the tree‐top ordering alternative. The tree‐top alternative is appropriate for one‐sided comparisons for treatments with a control. In the next set of models normality is assumed. In one such model k independent populations have different unknown means but have an unknown common variance. An independent estimate of the variance exists. We test homogeneity of means against the alternative of no homogeneity. We also consider the alternative of an ordering of the means as well as the tree‐top ordering. The final model considered is when we take a random sample from a multivariate normal population with unknown mean vector and an unknown covariance matrix of the intraclass type. We test the hypothesis that the mean vector is the zero vector against the one‐sided alternative that each mean is nonnegative (with at least one positive).