A complete statistic is a type of statistic that captures all the information available in a sample about a parameter of interest, meaning that no unbiased estimator can improve upon it. In essence, if a statistic is complete, any unbiased function of that statistic is also unbiased, which establishes a strong relationship with sufficiency and efficiency. The concept of completeness plays an important role in determining the admissibility of estimators and understanding how they behave in the context of estimation theory.
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