A Note on the Basu’s Theorem

Nayak Sinha (2012) showed the fact that any uniformly minimum variance unbiased estimator (UMVUE) which is uncorrelated with all the unbiased estimators of zero do require some uses of certain conclusions of the Rao-Blackwell and Lehmann-Scheffé theorems. They also showed that the conditional mean and variance of any UMVUE, given any ancillary statistic, must be independent of the ancillary. In this short paper, a new concept called H -sufficient statistic is introduced by which some of their results are generalized. We also obtain some new interpretations and well-known examples by the new concept. Finally, by using the Basu’s theorem, some new definitions and interpretations are introduced for UMVUE.