On Measuring the Conformity of a Parameter Set to a Trend, with Applications

摘要

Consider the hypothesis H(1):theta(1) > or = theta(2) > or = ... > or = theta(k) regarding a collection, theta(1), theta(2),...theta(k), of unknown parameters. It is clear that this trend is reflected in certain possible parameter sets more than in others. A quantification of this notion of conformity to a trend, which was suggested by Barlow and Brunk (1972), is studied. Applications of the resulting theory to several order restricted hypothesis tests are presented. (Author)