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An efficient family of robust-type estimators for the population variance in simple and stratified random sampling

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  • Tolga Zaman
  • Hasan Bulut

Abstract

In this study, we propose the robust ratio-type estimator of finite population variance considering the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance matrices in simple and stratified random sampling. The mean square errors (MSE) equations are obtained for the robust ratio-type estimator. The conditions for which the proposed robust ratio-type estimator is more efficient as compared to competing estimators have been discussed. The MCD and MVE are robust against outliers. Thus, when there is an outlier in the data, simulations and empirical results show that the proposed robust ratio-type estimators under simple and stratified random sampling have a lower mean square error than the traditional estimators. In addition, we support theoretical results with contaminated real examples and simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:8:p:2610-2624
    DOI: 10.1080/03610926.2021.1955388
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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