## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 43, Number 4 (1972), 1312-1316.

### Locally Best Invariant Test for Sphericity and the Limiting Distributions

#### Abstract

The locally best invariant test for testing sphericity in a multivariate normal distribution is obtained. It is different from the likelihood ratio criterion. Some other known results are remarked. The limiting distributions of the test statistics are investigated. In particular Pitman efficiency of the likelihood ratio test with respect to the locally best invariant test is shown to be one for normal alternatives.

#### Article information

**Source**

Ann. Math. Statist., Volume 43, Number 4 (1972), 1312-1316.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177692481

**Digital Object Identifier**

doi:10.1214/aoms/1177692481

**Mathematical Reviews number (MathSciNet)**

MR311032

**Zentralblatt MATH identifier**

0251.62036

**JSTOR**

links.jstor.org

#### Citation

Sugiura, Nariaki. Locally Best Invariant Test for Sphericity and the Limiting Distributions. Ann. Math. Statist. 43 (1972), no. 4, 1312--1316. doi:10.1214/aoms/1177692481. https://projecteuclid.org/euclid.aoms/1177692481