Window estimates of location and scale with applications to the cauchy distribution

Location and scale parameters are estimated via “window estimates”. The consistency and asymptotic normality of the estimates are established. The special case of the Cauchy distribution is considered, where the estimates are shown to have the same asymptotic distribution as the maximum-likelihood estimates. Additional applications are given for the Pearson type-VII distributions. The estimates have the advantages of ease of computation and high asymptotic efficiencies for certain heavy-tailed distributions.