## The Annals of Statistics

- Ann. Statist.
- Volume 22, Number 3 (1994), 1547-1554.

### Monotonicity Properties of the Power Functions of Likelihood Ratio Tests for Normal Mean Hypotheses Constrained by a Linear Space and a Cone

#### Abstract

Anderson studied the monotonicity of the integral of a symmetric, unimodal density over translates of a symmetric convex set. Restricting attention to elliptically contoured, unimodal densities, Mukerjee, Robertson and Wright weakened the assumption of symmetry on the set and obtained monotonicity properties of power functions, including unbiasedness, for some likelihood ratio tests in order restricted inference for the variance-known case. For elliptically contoured, unimodal densities, we weaken the assumption of convexity to obtain similar results in the case of unknown variances. The results apply to situations in which the null hypothesis is a linear space and the alternative is a closed, convex cone.

#### Article information

**Source**

Ann. Statist., Volume 22, Number 3 (1994), 1547-1554.

**Dates**

First available in Project Euclid: 11 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176325642

**Digital Object Identifier**

doi:10.1214/aos/1176325642

**Mathematical Reviews number (MathSciNet)**

MR1311989

**Zentralblatt MATH identifier**

0818.62056

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F03: Hypothesis testing

Secondary: 62H15: Hypothesis testing

**Keywords**

Anderson's inequality elliptically contoured densities order restricted inference unbiased tests

#### Citation

Hu, Xiaomi; Wright, F. T. Monotonicity Properties of the Power Functions of Likelihood Ratio Tests for Normal Mean Hypotheses Constrained by a Linear Space and a Cone. Ann. Statist. 22 (1994), no. 3, 1547--1554. doi:10.1214/aos/1176325642. https://projecteuclid.org/euclid.aos/1176325642