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A Comparative Study of New Ratio-Type Family of Estimators Under Stratified Two-Phase Sampling

Author

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  • Abdulaziz S. Alghamdi

    (Department of Mathematics, College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia)

  • Hleil Alrweili

    (Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia)

Abstract

Two-phase sampling is a useful technique for sample surveys, particularly when prior auxiliary data is not accessible. The ranks of the auxiliary variable often coincide with those of the research variable when two variables are correlated. By considering this relationship, we can significantly increase estimator accuracy. In this paper, we use the ranks of the auxiliary variable along with extreme values to estimate the population mean of the study variable. Up to a first-order approximation, we analyze the characteristics of the suggested class of estimators with an emphasis on biases and mean squared errors in stratified two-phase sampling. The theoretical results are verified using different datasets and a simulation study, which demonstrates that the proposed estimators outperform the existing ones in terms of percent relative efficiency.

Suggested Citation

  • Abdulaziz S. Alghamdi & Hleil Alrweili, 2025. "A Comparative Study of New Ratio-Type Family of Estimators Under Stratified Two-Phase Sampling," Mathematics, MDPI, vol. 13(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:327-:d:1572089
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    References listed on IDEAS

    as
    1. Rueda, M. M. & Arcos, A. & Martinez-Miranda, M. D. & Roman, Y., 2004. "Some improved estimators of finite population quantile using auxiliary information in sample surveys," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 825-848, May.
    2. Umer Daraz & Mohammed Ahmed Alomair & Olayan Albalawi & Abdulaziz S. Al Naim, 2024. "New Techniques for Estimating Finite Population Variance Using Ranks of Auxiliary Variable in Two-Stage Sampling," Mathematics, MDPI, vol. 12(17), pages 1-14, September.
    3. Saurav Guha & Hukum Chandra, 2021. "Improved estimation of finite population mean in two-phase sampling with subsampling of the nonrespondents," Mathematical Population Studies, Taylor & Francis Journals, vol. 28(1), pages 24-44, January.
    4. Umer Daraz & Jinbiao Wu & Olayan Albalawi, 2024. "Double Exponential Ratio Estimator of a Finite Population Variance under Extreme Values in Simple Random Sampling," Mathematics, MDPI, vol. 12(11), pages 1-11, June.
    5. Tolga Zaman & Cem Kadilar, 2021. "New class of exponential estimators for finite population mean in two-phase sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(4), pages 874-889, February.
    6. Mohammed Ahmed Alomair & Umer Daraz, 2024. "Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    7. Housila Singh & Mariano Ruiz Espejo, 2007. "Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 71-85.
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