## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 5 (1976), 1003-1011.

### A Condition Under Which the Pitman and Bahadur Approaches to Efficiency Coincide

#### Abstract

The approximate Bahadur efficiency and the Pitman efficiency for hypothesis testing problems are considered. A theorem is stated and proved which gives a condition under which the existence of the limiting (as the alternative approaches the hypothesis) approximate Bahadur efficiency implies the existence of the limiting (as the significance level approaches 0) Pitman efficiency and the equality of the two limits. Several examples are then given to show how the theorem may be used in computing previously unknown limiting Pitman efficiencies using the Bahadur approach.

#### Article information

**Source**

Ann. Statist., Volume 4, Number 5 (1976), 1003-1011.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343600

**Digital Object Identifier**

doi:10.1214/aos/1176343600

**Mathematical Reviews number (MathSciNet)**

MR440790

**Zentralblatt MATH identifier**

0351.62033

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G20: Asymptotic properties

Secondary: 62F20

**Keywords**

Bahadur efficiency Pitman efficiency

#### Citation

Wieand, Harry S. A Condition Under Which the Pitman and Bahadur Approaches to Efficiency Coincide. Ann. Statist. 4 (1976), no. 5, 1003--1011. doi:10.1214/aos/1176343600. https://projecteuclid.org/euclid.aos/1176343600