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New Techniques for Estimating Finite Population Variance Using Ranks of Auxiliary Variable in Two-Stage Sampling

Author

Listed:
  • Umer Daraz

    (School of Mathematics and Statistics, Central South University, Changsha 410017, China)

  • Mohammed Ahmed Alomair

    (Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Abdulaziz S. Al Naim

    (Accounting Department, Business School, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

Abstract

This article presents a new set of estimators designed to estimate the finite population variance of a study variable in two-phase sampling. These estimators utilize the information about extreme values and ranks of an auxiliary variable. Through a first-order approximation, we investigate the properties of these estimators, including biases and mean squared errors (MSEs). Furthermore, a comprehensive simulation study is conducted to assess their performance and validate our theoretical insights. Results demonstrate that our proposed class of estimators performs better in terms of percent relative efficiency (PRE) across various simulation scenarios compared to existing estimators. In addition, in the application section, we utilize three data sets to further validate the performance of our proposed estimators against conventional unbiased variance estimators, ratio and regression estimators, as well as other existing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2741-:d:1470231
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    References listed on IDEAS

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    1. Tolga Zaman & Hasan Bulut, 2023. "An efficient family of robust-type estimators for the population variance in simple and stratified random sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(8), pages 2610-2624, April.
    2. Housila Singh & Ramkrishna Solanki, 2013. "A new procedure for variance estimation in simple random sampling using auxiliary information," Statistical Papers, Springer, vol. 54(2), pages 479-497, May.
    3. 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.
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