- 著者
- Akahira M. Ohyauchi N.
- 出版者
- Taylor & Francis Group
- 雑誌
- Communications in statistics. Theory and methods (ISSN:03610926)
- 巻号頁・発行日
- vol.36, no.11, pp.2049-2059, 2007-08
- 被引用文献数
- 1 4
In non-regular cases when the regularity conditions does not hold, the Chapman–Robbins (1951) inequality for the variance of unbiased estimators is well known, but the lower bound by the inequality is not attainable. In this article, we extend the Kiefer-type information inequality applicable to the non-regular case to the asymptotic situation, and we apply it to the case of a family of truncated distributions, in which the lower bound by the Kiefer-type inequality derived from an appropriate prior distribution is attained by the asymptotically unbiased estimator. It also follows from the completeness of the sufficient statistic that the lower bound is asymptotically best. Some examples are also given.
- 著者
- Akahira M. Ohyauchi N.
- 出版者
- Taylor & Francis
- 雑誌
- Statistics : a journal of theoretical and applied statistics (ISSN:02331888)
- 巻号頁・発行日
- vol.41, no.2, pp.137-144, 2007-04
- 被引用文献数
- 3 9
From the Bayesian viewpoint, the information inequality applicable to the non-regular case is discussed. It is shown to construct an estimator which minimizes locally the variance of any estimator satisfying weaker conditions than the unbiasedness condition from which an information inequality is derived. The Hammersley–Chapman–Robbins inequality is also obtained as a special case of the inequality. An example is also given.