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We give a method of estimating parameters in the linear regression model which allowB the dependent variable to be censored and the residual distribution to be unspecified. The method differs from that of Miller (1976) in that the normal equations rather than the sum of squares of residuals are modified and this appears to overcome the inconsistency problems in Miller's approach. Large sample properties of the estimator of slope are derived heuristically and substantiated by simulations. Some of the heart transplant data reported and analysed by Miller are reanalysed using the present method.