## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 36, Number 1 (1965), 198-202.

### On the Estimation of Contrasts in Linear Models

Subha Bhuchongkul and Madan L. Puri

#### Abstract

In linear models with several observations per cell, a class of estimates of all contrasts are defined in terms of rank test statistics such as the Wilcoxon or normal scores statistic, which extend the results of Hodges and Lehmann (1963) and Lehmann (1963). The asymptotic efficiency of these estimates relative to the standard least squares estimates, as the number of observations in each cell gets large, is shown to be the same as the Pitman efficiency of the rank tests on which they are based to the corresponding $t$-tests.

#### Article information

**Source**

Ann. Math. Statist., Volume 36, Number 1 (1965), 198-202.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177700282

**Digital Object Identifier**

doi:10.1214/aoms/1177700282

**Mathematical Reviews number (MathSciNet)**

MR170416

**Zentralblatt MATH identifier**

0135.19504

**JSTOR**

links.jstor.org

#### Citation

Bhuchongkul, Subha; Puri, Madan L. On the Estimation of Contrasts in Linear Models. Ann. Math. Statist. 36 (1965), no. 1, 198--202. doi:10.1214/aoms/1177700282. https://projecteuclid.org/euclid.aoms/1177700282