Statistical Estimation for Truncated Exponential Families by Masafumi Akahira

Author:Masafumi Akahira
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

where . Then, it follows from (3.2), (3.4), and (3.12) that the solutions of of the following

become , , , respectively where . From (3.5), we obtain the bias-adjusted MLE using , , , and

with . From Theorem 3.6.1, we have the second-order asymptotic losses

as .

When , , and , the values of the second-order asymptotic loss and the ratio are obtained from the above and Remark 3.6.1 (see Table 3.4 and Fig. 3.4).

Table 3.4Values of and for and

1 / 2

2 / 3

5 / 6

Fig. 3.4Graph of the ratio up to the order 1 / n for and

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