## 統計学輪講（第３４回）

日時 2000年11月21日(火) 15時00分〜16時40分
場所 経済学部5階視聴覚室
講演者 藤澤 洋徳 (東工大)
演題 Asymptotic Properties of Conditional Maximum Likelihood Estimator
In a Certain Exponential Model
概要
The conditional maximum likelihood estimator is suggested
as an alternative to the maximum likelihood estimator and
is favorable for an estimator of a dispersion parameter
in the normal distribution, the inverse-gaussian distribution,
and so on. However, it is not clear whether the conditional maximum
likelihood estimator is asymptotically efficient in general.
Consider the case where it is asymptotically efficient and
its asymptotic covariance depends only on an objective parameter
in an exponential model. This remand implies that the exponential
model possesses a certain parallel foliation. In this situation,
this paper investigates asymptotic properties of the conditional
maximum likelihood estimator and compares the conditional maximum
likelihood estimator with the maximum likelihood estimator.
We see that the bias of the former is more robust than that of
the latter and that two estimators are very close, especially
in the sense of bias-corrected version.
The mean Pythagorean relation is also discussed.
発表内容は，10月中旬に統数研で行なわれたシンポジウムにおいて
私が発表した内容とほぼ同じです．

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