Second Order Admissibilities in Multi-parameter Logistic Regression Model

In multi-parameter family of distributions, conditions for a modified maximum likelihood estimator to be second order admissible are given. Applying these results to the multi-parameter logistic regression model, it is shown that the maximum likelihood estimator is always second order inadmissible. Also, conditions for the Berkson estimator to be second order admissible are given.

Authors:

• Chie Obayashi
• Hidekazu Tanaka
• Yoshiji Takagi

Keywords:

• Berkson estimator
• modified maximum likelihood estimator
• Multi-parameter logistic regression model
• second order admissibility.

References:

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Amer. Statist. Assoc., vol. 50, pp. 130-162, 1955.
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pp. 488-505, 1980.
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for second order admissibility with applications to Berkson-s bioassay
problem," Ann. Statist., vol. 9, pp. 1334-1338, 1981.
[4] H. Tanaka, C. Obayashi and Y. Takagi, "On second order admissibilities
in two-parameter logistic regression model," submitted for publication.
[5] K. Takeuchi and M. Akahira, "Asymptotic optimality of the generalized
Bayes estimator in multiparameter cases," Ann. Inst. Statist. Math., vol.
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