When is a statistic insufficient according to the factorization theorem?

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SUMMARY

The discussion centers on the concept of sufficiency in statistics, specifically in relation to the factorization theorem. An example provided illustrates that the average of the first three observations from a sample of N>3 is insufficient for estimating the overall mean of the sample. This highlights the importance of considering the entire dataset when making statistical inferences. The factorization theorem serves as a critical tool for determining the sufficiency of statistics in relation to parameters.

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  • Understanding of the factorization theorem in statistics
  • Knowledge of statistical sufficiency and its definitions
  • Familiarity with sample statistics and their applications
  • Basic concepts of parameter estimation
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  • Study the applications of the factorization theorem in various statistical models
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Statisticians, data analysts, and students studying statistical inference who seek to deepen their understanding of sufficiency and the factorization theorem.

roadworx
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Can anyone give me an example of when a statistic is insufficient, using the factorization theorem, if possible?

Thanks.
 
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You need to remember that sufficiency is defined with respect to a parameter and a sample. "The average of the first three observations out of a sample of N>3 observations" is clearly insufficient for calculating the overall mean from the same sample.
 

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