a note on the basu’s theorem

Nayak & sinha (2012) showed the fact that any uniformly minimum varianceunbiased estimator (umvue) which is uncorrelated with all the unbiased estimatorsof zero do require some uses of certain conclusions of the rao-blackwell andlehmann-scheffé theorems. they also showed that the conditional mean and varianceof 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 whichsome of their results are generalized. we also obtain some new interpretations andwell-known examples by the new concept. finally, by using the basu’s theorem, somenew definitions and interpretations are introduced for umvue.