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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY It is well known that a M-estimator of the centre of symmetry 0 of a symmetric distribution can be defined in terms of either a continuous symmetric loss function p or the associated influence function qi. This estimator is robust if qf is bounded. In this paper, we develop a generalization of the M-concept to estimation of a quantile analogue of 0, called a M-quantile, by introducing a particular kind of asymmetry into qi. A natural consequence is that the M-quantile parameter then bears the same relationship to 0 as the ordinary quantile bears to the median. The extension of this idea to the case of multivariate data is considered in some detail. Two applications to the analysis of agricultural survey data are given.

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