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In statistics, Basu's theorem states that any boundedly complete minimal sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu. It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the section below. This property (independence of sample mean and sample variance) characterizes normal distributions.

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  • Sätze von Basu (de)
  • Basu's theorem (en)
  • 巴苏定理 (zh)
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  • Die Sätze von Basu sind drei Aussagen der mathematischen Statistik, die eine Verbindung zwischen der Suffizienz, der Vollständigkeit und der Verteilungsfreiheit herstellen. Sie wurden 1955 durch Debabrata Basu aufgestellt und bewiesen. (de)
  • In statistics, Basu's theorem states that any boundedly complete minimal sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu. It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the section below. This property (independence of sample mean and sample variance) characterizes normal distributions. (en)
  • 在统计学中，巴苏定理（Basu's Theorem）指出任何有界完全的充分统计量与任何辅助统计量独立。 这是Debabrata Basu于1955年发现的结论。 (zh)
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  • Die Sätze von Basu sind drei Aussagen der mathematischen Statistik, die eine Verbindung zwischen der Suffizienz, der Vollständigkeit und der Verteilungsfreiheit herstellen. Sie wurden 1955 durch Debabrata Basu aufgestellt und bewiesen. (de)
  • In statistics, Basu's theorem states that any boundedly complete minimal sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu. It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the section below. This property (independence of sample mean and sample variance) characterizes normal distributions. (en)
  • 在统计学中，巴苏定理（Basu's Theorem）指出任何有界完全的充分统计量与任何辅助统计量独立。 这是Debabrata Basu于1955年发现的结论。 (zh)
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