## The Annals of Statistics

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

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

Tim Robertson and F. T. Wright

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62F03: Hypothesis testing

Secondary: 62E15: Exact distribution theory

**Keywords**

Order restricted inference tests for and against a trend isotonic inference Chi-bar-squared distribution least favorable configurations

#### Citation

Robertson, Tim; Wright, F. T. On Measuring the Conformity of a Parameter Set to a Trend, with Applications. Ann. Statist. 10 (1982), no. 4, 1234--1245. doi:10.1214/aos/1176345988. https://projecteuclid.org/euclid.aos/1176345988