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.
"On Measuring the Conformity of a Parameter Set to a Trend, with Applications." Ann. Statist. 10 (4) 1234 - 1245, December, 1982. https://doi.org/10.1214/aos/1176345988