Mathematical Statistics Lesson of the Day – Ancillary Statistics
June 23, 2015 1 Comment
Suppose that you collected data
in order to estimate a parameter . Let be the probability density function (PDF) or probability mass function (PMF) for .
be a statistics based on .
If the distribution of does NOT depend on , then is called an ancillary statistic.
An ancillary statistic contains no information about ; its distribution is fixed and known without any relation to . Why, then, would we care about I will address this question in later Statistics Lessons of the Day, and I will connect ancillary statistics to sufficient statistics, minimally sufficient statistics and complete statistics.