Mathematical Statistics Lesson of the Day – Complete Statistics
November 27, 2014 1 Comment
Suppose that you collected data
in order to estimate a parameter . Let be the probability density function (PDF)* for .
be a statistic based on .
then is said to be complete. To deconstruct this esoteric mathematical statement,
- let be a measurable function
- if you want to use to form an unbiased estimator of the zero function,
- and if the only such function is almost surely equal to the zero function,
- then is a complete statistic.
I will discuss the intuition behind this bizarre definition in a later Statistics Lesson of the Day.
*This above definition holds for discrete and continuous random variables.