publication . Article . 2001

ASYMPTOTIC COMPARISONS OF U-STATISTICS, V-STATISTICS AND LIMITS OF BAYES ESTIMATES BY DEFICIENCIES

Toshifumi, Nomachi; Hajime, Yamato; Graduate School of Science and Engineering, Kagoshima University:Miyakonojo College of Technology; Faculty of Science, Kagoshima University;
Open Access
  • Published: 01 Jun 2001 Journal: JOURNAL OF THE JAPAN STATISTICAL SOCIETY, volume 31, pages 85-98 (issn: 1882-2754, eissn: 1348-6365, Copyright policy)
  • Publisher: The Japan Statistical Society
Abstract
As estimators of estimable parameters, we consider three statistics which are U-statistic, V-statistic and limit of Bayes estimate. This limit of Bayes estimate, called LB-statistic in this paper, is obtained from Bayes estimate of estimable parameter based on Dirichlet process, by letting its parameter tend to zero. For the estimable parameter with non-degenerate kernel, the asymptotic relative efficiencies of LB-statistic with respect to U-statistic and V-statistic and that of V-statistic with respect to U-statistic are equal to one. We show asymptotic differences among LB-statistic, U-statistic and V-statistic by using the deficiency.
Subjects
free text keywords: Mathematics, Kernel (linear algebra), Statistics, Bayes' theorem, Estimator, Dirichlet process, Efficiency, Estimable parameter, Kernel, Degree
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publication . Article . 2001

ASYMPTOTIC COMPARISONS OF U-STATISTICS, V-STATISTICS AND LIMITS OF BAYES ESTIMATES BY DEFICIENCIES

Toshifumi, Nomachi; Hajime, Yamato; Graduate School of Science and Engineering, Kagoshima University:Miyakonojo College of Technology; Faculty of Science, Kagoshima University;