An Interpretation of Completeness and Basu's Theorem
本文试图将充分统计量T的完备性刻画为所有辅助统计量与T独立的条件，虽不成立，但通过修改辅助性或完备性定义得到两个正确版本，并讨论了完备性的含义及缺乏完备性时的困难。
Abstract In order to obtain a statistical interpretation of completeness of a sufficient statistic T, an attempt is made to characterize this property as equivalent to the condition that all ancillary statistics are independent of T. For technical reasons, this characterization is not correct, but two correct versions are obtained in Section 3 by modifying either the definition of ancillarity or of completeness. The light this throws on the meaning of completeness is discussed in Section 4. Finally, Section 5 reviews some of the difficulties encountered in models that lack completeness.