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JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Vol. 26 (1996) No. 1 P 101-117

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http://doi.org/10.14490/jjss1995.26.101


Takeuchi [37], Takeuchi and Akahira [38] and Pfanzagl [27] among others proved that any first-order efficient estimators are second-order efficient. Many other authors e. g., Ghosh [15], have conjectured that any third-order efficient estimators are also fourth-order efficient. Based on the concentration probability of estimators about a true parameter, this paper gives a positive answer to the conjecture in a curved exponential family with multi-structural parameters. It is seen that choice of bias-correction factors is critical.

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