Estimation of location and scale parameters of a distribution by U-statistics based on best linear functions of order statistics

In this work we propose a technique of estimating the location parameter μ and scale parameter σ of a distribution by U-statistics constructed by taking best linear functions of order statistics as kernels. The method has been illustrated for estimating the location and scale parameters of type-I extreme value distribution. We have computed the asymptotic relative efficiencies of the proposed U-statistics with the appropriate maximum likelihood estimators based on samples drawn from each of type-I extreme value, logistic and normal distributions. In all cases very high asymptotic relative efficiencies are obtained.