ABSTRACT
Let X be the sample space and let A be the s -algebra of subsets of X, and let P?,
be the probability on (X, A), where O is an interval in EP. Let D be the set of all possible estimators of ?. A function
defined on O×D, represents the loss of erroneously estimating ? by d. (It may be remarked that d is a vector quantity.) Let
where fX(x|?) denotes the probability density function of X with values corresponding to P? with respect to the Lebesgue measure dx. R(?, d) is called the
risk function of the estimator for the parameter Let h(?), denote the prior probability density on O. The posterior probability density function of ? given that X=x is given by
