A sufficient statistic for a parameter 
is a statistic 
that retains all information in the sample 
about 
. Formally, the conditional distribution
of 
given 
does not depend on 
.
For a dominated family with probability density function 
, the Fisher-Neyman
factorization theorem states that 
is sufficient iff
 |
for suitable nonnegative functions 
and 
. The Rao-Blackwell theorem
improves an estimator by taking its conditional
expectation given a sufficient statistic.
