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 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Basu's Theorem (Wikipedia)
Sources
1. Basu's Theorem (Wikipedia)
Wikimedia FoundationLead paragraph
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.
In Branch: Probability and Statistics, Lead sentence
In statistics, Basu's theorem states that any boundedly complete and sufficient statistic is independent of any ancillary statisti
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