Robust estimation of shift parameters with a limited noise variance

In discussing robust estimation of the shift parameter (distribution center) for symmetrical planes the attention is focused on problems where the variance is constrained. The resultant solutions are used in the case of densities of the blend type. The nature of the solution is shown to be dictated by the constraint value in that with small variances Gaussian densities and the associated least squares algorithms of data processing are optimal with large variances the Laplacean density and least module algorithms area.