多个正态总体均值与标准差比在简单树序约束下的最大似然估计

Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations under Treeorder Restriction

JI Yonggang¹, LI Shuyou¹, ZHAO Shishun², SHI Haifang²

1. Department of Mathematics and Physics, Liaoning University of Technology, Jinzhou 121001, Liaoning Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2007-11-18 Revised:1900-01-01 Online:2008-09-26 Published:2008-09-26
Contact: LI Shuyou

Abstract

Abstract: For knormal populations with unknown means μ_i and variances σ²_i>0 (i=1,2,…,k), it is assumedthat there is a treeorder restriction between ratios of means and standard deviations. According to the method of isotonic regression, a procedure of obtaining the maximum likelihood estimators of μ_i's and σ_i's under the treeorder restrictions is proposed. In the case of k=7, some connected results and simulationresultsare given.

Key words: simple treeorder, maximum likelihood estimator, lik elihood function, iteration method

CLC Number:

O212.1

JI Yonggang, LI Shuyou, ZHAO Shishun, SHI Haifang. Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations under Treeorder Restriction[J].J4, 2008, 46(05): 829-835.

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Maximum Likelihood Estimation of Ratios of Means and Standard Deviations from Normal Populations under Treeorder Restriction

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