## The Annals of Statistics

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

#### 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.

#### Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1234-1245.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345988

Digital Object Identifier
doi:10.1214/aos/1176345988

Mathematical Reviews number (MathSciNet)
MR673658

Zentralblatt MATH identifier
0512.62033

JSTOR