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Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

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Abstract

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming. In the current paper, a modification of ranked set sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the location parameter for location family. A maximum likelihood estimator (MLE) of the location parameter for this family is studied and its properties are obtained. We prove that the MLE is an equivariant estimator under location transformation. In order to give more insight into the performance of MERSS with respect to (w.r.t.) simple random sampling (SRS), the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for some usual location distributions. The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.

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Change history

  • 02 February 2021

    The first author should be Chen instead of Chein.

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Acknowledgments

The authors thank the Editor in Chief, an associate editor and reviewers for their valuable comments and suggestions to improve the paper.

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Authors and Affiliations

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

    Wang-xue Chen, Chun-xian Long, Rui Yang & Dong-sen Yao

Authors
  1. Wang-xue Chen
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  2. Chun-xian Long
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  3. Rui Yang
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  4. Dong-sen Yao
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Corresponding author

Correspondence to Wang-xue Chen.

Additional information

This paper is supported by the National Natural Science Foundation of China (No.11901236), the Scientific Research Fund of Hunan Provincial Science and Technology Department (No.2019JJ50479), the Scientific Research Fund of Hunan Provincial Education Department(No. 18B322), the Young Core Teacher Foundation of Hunan Province (No. [2020]43) and the Fundamental Research Fund of Xiangxi Autonomous Prefecture (No. 2018SF5026).

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Chen, Wx., Long, Cx., Yang, R. et al. Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design. Acta Math. Appl. Sin. Engl. Ser. 37, 101–108 (2021). https://doi.org/10.1007/s10255-021-0998-8

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  • DOI: https://doi.org/10.1007/s10255-021-0998-8

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