# Mathematical Statistics Lesson of the Day – Ancillary Statistics

June 23, 2015 1 Comment

The set-up for today’s post mirrors my earlier Statistics Lessons of the Day on sufficient statistics and complete statistics.

Suppose that you collected data

in order to **estimate** a **parameter** . Let be the **probability density function (PDF)** or** probability mass function (PMF)** for .

Let

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.

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