Basu's Theorem states that if a statistic is complete and sufficient for a parameter, then it is statistically independent of every ancillary statistic, one whose own distribution does not depend on that parameter. Named for Debabrata Basu, it is a standard tool of mathematical statistics for proving independence between two statistics without computing their joint distribution directly, often used to simplify variance calculations in sampling theory.
Facts
StatementIf a statistic is boundedly complete and sufficient for a parameter, it is statistically independent of every ancillary statistic for that same parameter. Debabrata Basu proved the result in 1955. 1 Sources
1. Basu's Theorem (Wikipedia)
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In statistics, Basu's theorem states that any boundedly complete and sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu.
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