Optimal allocation for estimating the correlation coefficient of Morgenstern type bivariate exponential distribution by ranked set sampling with concomitant variable
Optimal allocation for estimating the correlation coefficient of Morgenstern type bivariate exponential distribution by ranked set sampling with concomitant variable
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DOI：
10.1007/s11424-013-0040-1
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发表时间：
2013-04
影响因子：
2.1
通讯作者：
M. Xie;Ming Xiong;Ming Wu
中科院分区：
文献类型：
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作者：
M. Xie;Ming Xiong;Ming Wu
只要可以通过学习变量或辅助变量的判断方法容易地完成一组样本单元的排序，就可以应用排序的集合样本。本文考虑基于与研究变量Y相关的辅助变量X的排序集样本，其中(X，Y)服从Morgenstein型二元指数分布。讨论了用辅助变量X对样本单位进行排序，用研究变量Y估计相关系数时，随机变量X和Y的相关系数ρ的无偏估计的最优配置问题。本文首先给出了当研究变量Y的平均ρ已知时，θ的一类无偏估计，并得到了这类估计的一个本质完备子类。进一步，在这个子类中找到了无偏估计的最优配置，并证明了它是贝叶斯估计、可容许估计和极大极小估计。最后，将已知ρ下最优分配下的θ无偏估计改进为ρ未知情况下的θ估计，并证明了改进后的估计具有强相合性。
Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variableXwhich is correlated with the study variableY, where (X, Y) follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficientρof the random variablesXandYwhen the auxiliary variableXis used for ranking the sample units and the study variableYis measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators ofρwhen the meanθof the study variableYis known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator ofρunder the optimal allocation in the case of knownθis reformed for estimatingρin the case of unknownθ, and the reformed estimator is shown to be strongly consistent.