## The Annals of Mathematical Statistics

### Null Distribution and Bahadur Efficiency of the Hodges Bivariate Sign Test

#### Abstract

This note presents a simplified expression for the exact null distribution of the Hodges bivariate sign test. The form is suitable for computing both for small and large sample size and gives the limiting distribution easily. A small table is given for the limiting distribution. The Bahadur limiting efficiency of the test is computed relative to the bivariate Hotelling $T^2$ test for normal alternatives. The value $2/\pi$ is obtained, which is the same as for the one dimensional sign test relative to the $t$-test.

#### Article information

Source
Ann. Math. Statist., Volume 33, Number 2 (1962), 803-807.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704600

Digital Object Identifier
doi:10.1214/aoms/1177704600

Mathematical Reviews number (MathSciNet)
MR137240

Zentralblatt MATH identifier
0124.10403

JSTOR