On Measuring the Conformity of a Parameter Set to a Trend, with Applications
The Annals of Statistics · 1982 · Volume 10 · Issue 4
Abstract
Consider the hypothesis $H_1: \theta_1 \geq \theta_2 \geq \cdots \geq \theta_k$ regarding a collection, $\theta_1, \theta_2, \cdots, \theta_k$, 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 is studied. Applications of the resulting theory to several order restricted hypothesis tests are presented.
Keywords
62E15, 62F03, Chi-bar-squared distribution, isotonic inference, least favorable configurations, Order restricted inference, tests for and against a trend
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