Efficient Estimation of Parameters of a Uniform Distribution in the Presence of Outliers by Ulhas Jayram Dixit, M. Masoom Ali and Jungsoo Woo

The uniformly minimum variance unbiased estimator (UMVUE) and the maximum likelihood estimator (MLE) are derived for samples from uniform distribution in the presence of outliers, where outliers are generated from generalized uniform distribution (GUD), when one parameter of the GUD is known. In this case it has been shown that UMVUE is better than MLE. When both the parameters are unknown then we have given a mixture of estimates, which is equally efficient as MLE, but easier to handle than MLE. Moreover, we have shown that mixture estimates are consistent.