## The Annals of Statistics

### Rank Regression

Jack Cuzick

#### Abstract

An estimation procedure for $(b, g)$ is developed for the transformation model $g(Y) = bz + \text{error, where} g$ is an unspecified strictly increasing function. The estimator for $b$ can be viewed as a hybrid between an $M$-estimator and an $R$-estimator. It differs from an $M$-estimator in that the dependent variable is replaced by a score based on ranks and from an $R$-estimator in that the ranks of dependent variable itself are used, not the ranks of the residuals. This provides robustness against the scale on which the variables are thought to be linearly related, as opposed to robustness against misspecification of the error distribution. Existence, uniqueness, consistency and asymptotic normality are studied.

#### Article information

Source
Ann. Statist. Volume 16, Number 4 (1988), 1369-1389.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176351044

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176351044

Mathematical Reviews number (MathSciNet)
MR964929

Zentralblatt MATH identifier
0653.62031

Subjects
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression 62G30: Order statistics; empirical distribution functions

#### Citation

Cuzick, Jack. Rank Regression. Ann. Statist. 16 (1988), no. 4, 1369--1389. doi:10.1214/aos/1176351044. http://projecteuclid.org/euclid.aos/1176351044.