Generalized Blackwell-Rao and Cramer-Rao's inequalities

Abstract

The first part of the paper is devoted to the definition and the existence of the conditional expectation of statistic. Then we have established the Blackwell-Rao's inequality. After that we have given the definition of the Fisher information operator. We subsequently have established the important property of the information operator that the only statistic which reduces data in the sample without losing information is the sufficient statistic. Afterwards we have proved the Cramer-Rao inequality.