对称熵损失下两个指数总体均值的序约束估计

对称熵损失下两个指数总体均值的序约束估计

赵世舜¹, 宋洋¹, 宋立新²

1. 吉林大学数学研究所, 长春 130012; 2. 大连理工大学应用数学系, 辽宁省大连 116024

收稿日期:2006-03-06 修回日期:1900-01-01 出版日期:2007-01-26 发布日期:2007-01-26
通讯作者: 赵世舜

Estimation of Order Means of Two Sample DistributionExponential under Symmetric Entropy Loss

ZHAO Shi shun¹, SONG Yang¹, SONG Li xin²

1. Institute of Mathematics, Jilin University, Changchun 130012, China;2. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

Received:2006-03-06 Revised:1900-01-01 Online:2007-01-26 Published:2007-01-26
Contact: ZHAO Shi shun

摘要/Abstract

摘要： 在对称熵损失下, 讨论了样本容量相等时, 两个指数总体均值λ_i(i=1,2)的约束极大似然估计i的险, 其中约束为λ₁≤λ₂. 证明了λ₁与λ₂具有比经典极大似然估计X₁与X₂ 更小的风险, 并给出了当λ₂/λ₁→∞和n→∞时,λ_i对X_i(i=1,2)渐近功效e(λ_i,X_i)的值.

关键词: 序约束, 对称熵损失, 功效, 约束极大似然估计

Abstract: The present paper consider risk of the restricted maximum likelihood estimators (RMLE) of order means of two sample distribution exponential, λ₁≤λ₂, with the same sample size, under symmetric entropy loss. It proved that RMLE λ_i have smaller risk than usual sample means X_i(i=1,2). The asymptotic efficiencies e(λ_i,X_i) of RMLE λ_i with respect to sample means X_i for λ₂/λ₁→∞ and n→∞ have also been discussed.

Key words: order restriction, symmetric entropy loss, efficiency, restricted maximun likelihood estimator

中图分类号:

O212.1

赵世舜, 宋洋, 宋立新. 对称熵损失下两个指数总体均值的序约束估计[J]. J4, 2007, 45(01): 44-48.

ZHAO Shi shun, SONG Yang, SONG Li xin. Estimation of Order Means of Two Sample DistributionExponential under Symmetric Entropy Loss[J]. J4, 2007, 45(01): 44-48.

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