Summary
The optimality of estimation method is investigated in a curved exponential family. A risk function, which is an extension of a residual sum of squares in regression analysis, is introduced. It is shown that second order efficiency of an estimation method is equivalent to attain the minimum among limiting risks of all estimation methods.
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Eguchi, S. A characterization of second order efficiency in a curved exponential family. Ann Inst Stat Math 36, 199–206 (1984). https://doi.org/10.1007/BF02481964
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DOI: https://doi.org/10.1007/BF02481964