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For the usual multivariate linear model, preliminary test Mestimation theory is considered in an isotonic setup. Roy's union-intersection principle is incorporated in a formulation of suitable isotonic M-procedures for the preliminary testing component, following which M-estimator of location are presented in the same vein. The main thrust is on the development of the related asymptotic theory with a view to studying the allied robustness aspects. A numerical illustration is set to demonstrate the superiority of the proposed approach.

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