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Large sample properties of modified maximum likelihood estimator of the location parameter using moving extremes ranked set sampling

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  • Wang, Han
  • Chen, Wangxue

Abstract

The maximum likelihood estimator (MLE) obtained using moving extremes ranked set sampling (MERSS) typically does not have a closed form expression. In this study, we investigate a modified MLE (MMLE) utilizing MERSS for estimating the location parameter of a location family and analyze its properties in large samples. We derive the explicit form of the MMLE for two common distributions when MERSS is employed. The numerical results from two usual distributions indicate that the MMLE using MERSS is more efficient than that the MLE using simple random sampling with an equivalent sample size. The numerical results also indicate the loss of efficiency in using the MMLE under MERSS instead of the MLE under MERSS is very small for small values of m. Additionally, we examine the implications of imperfect ranking and demonstrate our approach using a real dataset.

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  • Wang, Han & Chen, Wangxue, 2025. "Large sample properties of modified maximum likelihood estimator of the location parameter using moving extremes ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 223(C).
    • Handle: RePEc:eee:stapro:v:223:y:2025:i:c:s0167715225000756
    DOI: 10.1016/j.spl.2025.110430
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    References listed on IDEAS

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    1. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    2. Guoxin Qiu & Abbas Eftekharian, 2021. "Extropy information of maximum and minimum ranked set sampling with unequal samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(13), pages 2979-2995, July.
    3. Omer Ozturk & N. Balakrishnan, 2009. "An Exact Control-Versus-Treatment Comparison Test Based on Ranked Set Samples," Biometrics, The International Biometric Society, vol. 65(4), pages 1213-1222, December.
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