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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Jishou University, Jishou, 416000, China

    Wangxue Chen

  2. Department of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Yi Tian & Minyu Xie

Authors
  1. Wangxue Chen
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  2. Yi Tian
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  3. Minyu Xie
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Corresponding author

Correspondence to Wangxue Chen.

Additional information

This research was supported by the National Science Foundation of China under Grant Nos. 11571133 and 11461027, and the Fundamental Research Funds for the Central Universities under Grant No. 20205001515.

This paper was recommended for publication by Editor XU Jin.

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Chen, W., Tian, Y. & Xie, M. Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling. J Syst Sci Complex 30, 1350–1363 (2017). https://doi.org/10.1007/s11424-017-6135-3

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  • DOI: https://doi.org/10.1007/s11424-017-6135-3

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