IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v224y2025ics0167715225001002.html

3 × 3 optimal ranked set sampling design with k cycles and best linear invariant estimators of the parameters for normal distribution

Author

Listed:
  • Li, Minmin
  • Chen, Wangxue

Abstract

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. Cost effective sampling will be an important research problem. In this article, we find a 3 × 3 optimal ranked set sampling (RSS) design with k cycles for the normal distribution N(μ,σ2) in which the location parameter μ and the scale parameter σ are both unknown based on the D–optimal criterion in the experimental design. Then, the best linear invariant estimates (BLIEs) of μ and σ from N(μ,σ2) and their properties are studied under this RSS design. The efficiency is compared by the determinant of the mean square error matrix. The theoretical results and numerical results show that the BLIEs under the optimal RSS are more effective than the BLIEs under the balanced RSS.

Suggested Citation

  • Li, Minmin & Chen, Wangxue, 2025. "3 × 3 optimal ranked set sampling design with k cycles and best linear invariant estimators of the parameters for normal distribution," Statistics & Probability Letters, Elsevier, vol. 224(C).
    • Handle: RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225001002
    DOI: 10.1016/j.spl.2025.110455
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715225001002
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2025.110455?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.
    2. 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.
    3. 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.
    4. Walid Abu-Dayyeh & Aissa Assrhani & Kamarulzaman Ibrahim, 2013. "Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling," Statistical Papers, Springer, vol. 54(1), pages 207-225, February.
    5. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wenchen Dai & Wangxue Chen & Honglve Zhao, 2025. "Estimation of the population mean under imperfect simple Z ranked set sampling," Statistical Papers, Springer, vol. 66(4), pages 1-22, June.
    2. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.
    3. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    4. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    5. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, February.
    6. Yang, Rui & Chen, Wangxue, 2025. "Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 226(C).
    7. 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).
    8. Barabesi, Lucio & El-Sharaawi, Abdel, 2001. "The efficiency of ranked set sampling for parameter estimation," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 189-199, June.
    9. Sanku Dey & Mahdi Salehi & Jafar Ahmadi, 2017. "Rayleigh distribution revisited via ranked set sampling," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 69-85, April.
    10. Dinesh S. Bhoj, 2001. "Ranked Set Sampling with Unequal Samples," Biometrics, The International Biometric Society, vol. 57(3), pages 957-962, September.
    11. Raqab, Mohammad Z. & Kouider, Elies & Al-Shboul, Qasim M., 2002. "Best linear invariant estimators using ranked set sampling procedure: comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 97-105, March.
    12. Xinlei Wang & Ke Wang & Johan Lim, 2012. "Isotonized CDF Estimation from Judgment Poststratification Data with Empty Strata," Biometrics, The International Biometric Society, vol. 68(1), pages 194-202, March.
    13. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    14. Oualid Saci & Megdouda Ourbih-Tari & Leila Baiche, 2023. "Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 540-571, February.
    15. H. M. Barakat & Haidy A. Newer, 2022. "Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size," Statistical Papers, Springer, vol. 63(6), pages 1801-1827, December.
    16. Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.
    17. Wangxue Chen & Rui Yang & Dongsen Yao & Chunxian Long, 2021. "Pareto parameters estimation using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 62(3), pages 1195-1211, June.
    18. Zeinab Akbari Ghamsari & Ehsan Zamanzade & Majid Asadi, 2024. "Using nomination sampling in estimating the area under the ROC curve," Computational Statistics, Springer, vol. 39(5), pages 2721-2742, July.
    19. Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    20. Arnold, Barry C. & Castillo, Enrique & María Sarabia, José, 2009. "On multivariate order statistics. Application to ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4555-4569, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225001002. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.