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December, 1988 Rank Regression
Jack Cuzick
Ann. Statist. 16(4): 1369-1389 (December, 1988). DOI: 10.1214/aos/1176351044


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.


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Jack Cuzick. "Rank Regression." Ann. Statist. 16 (4) 1369 - 1389, December, 1988.


Published: December, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0653.62031
MathSciNet: MR964929
Digital Object Identifier: 10.1214/aos/1176351044

Primary: 62G05
Secondary: 62G30, 62J05

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 4 • December, 1988
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