Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

作者：Chen, Wangxue^*; Tian, Yi; Xie, Minyu

来源：Journal of Systems Science and Complexity, 2017, 30(6): 1350-1363.

DOI：10.1007/s11424-017-6135-3

• Complete sufficient statistic
• continuous one-parameter exponential family
• maximum likelihood estimator
• ranked set sampling

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

• 出版日期2017-12
• 单位吉首大学; 华中师范大学