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본 논문에서는 단위행렬을 갖는 다변량 정규분포의 모평균 벡터를 추정하는 문제를 다루었다. 두 추정량을 비교하는데 균형 손실함수와 관련된 위험함수를 사용하였다. 린드리(Lindley) 형태의 추정량을 개량하는 다항식 형태의 추정량들이 스타인(Stein) 항등식과 Benkhaled et. al.의 방법으로 유도되었다. 각각의 개량된 추정은 다항식의 차수 증가를 이용하여 이전 것보다 더 개량된 추정량이 된다. 이들 추정량들은 모두 최대 가능도 추정량 (MLE)을 개량하기 때문에 최소최대의 성질을 갖는다. 모의실험 연구로서 그래프들과 표들을 매스매티카 프로그램에 의하여 제시하였다. 그러한 과정을 통해 개량된 추정량이 이전 추정량 보다 우수한 것을 확인하였다.
In this paper, the problem of estimating a multivariate normal mean vector with identity covariance matrix is considered. The risk associated with the balanced loss function is used to compare two estimators. A series of estimators with polynomial forms dominating Lindley type estimator is derived using the Stein’s identity and a technique of Benkhaled et. al.. Each improved estimator is better than previous one using the increase of degree of polynomial. These estimators are mimimax because they dominate the maximum likelihood estimator(MLE). As a simulation study some graphs and tables are presented by using Mathematica programs. Through such a process, it is confirmed that the improved estimators dominate the previous estimators.
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- Publisher :The Society of Convergence Knowledge
- Publisher(Ko) :융복합지식학회
- Journal Title :The Society of Convergence Knowledge Transactions
- Journal Title(Ko) :융복합지식학회논문지
- Volume : 10
- No :2
- Pages :93-108
- DOI :https://doi.org/10.22716/sckt.2022.10.2.018