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Robust Ratio- and Product-Type Estimators Under Non-normality via Linear Transformation Using Certain Known Population Parameters

Author

Listed:
  • Sanjay Kumar

    (Central University of Rajasthan)

  • Shivanshu Kumar

    (Central University of Rajasthan)

  • Evrim Oral

    (LSUHSC School of Public Health, Biostatistics Program)

Abstract

In the literature, a linear transformation on an auxiliary variable has been widely used to increase the efficiencies of ratio- and product-type estimators. However, additional information of unknown population parameters is required to utilize such estimators. In this paper, we propose two novel ratio-type and two novel product-type estimators under non-normality using the minimum and maximum values of the auxiliary variable. The expressions for mean square errors and biases for the proposed estimators are derived. We also calculate confidence intervals of the estimators. Theoretical results are supported using simulation studies. We also illustrate our results using a real life application of a body fat data set. We study robustness properties of the proposed estimators. We show that the proposed ratio-type estimators which utilize certain known auxiliary information can improve some other existing estimators which do not utilize such auxiliary information.

Suggested Citation

  • Sanjay Kumar & Shivanshu Kumar & Evrim Oral, 2021. "Robust Ratio- and Product-Type Estimators Under Non-normality via Linear Transformation Using Certain Known Population Parameters," Annals of Data Science, Springer, vol. 8(4), pages 733-753, December.
    • Handle: RePEc:spr:aodasc:v:8:y:2021:i:4:d:10.1007_s40745-020-00258-0
    DOI: 10.1007/s40745-020-00258-0
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    References listed on IDEAS

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    1. Cem Kadilar & Yesim Unyazici & Hulya Cingi, 2009. "Ratio estimator for the population mean using ranked set sampling," Statistical Papers, Springer, vol. 50(2), pages 301-309, March.
    2. Oral, Evrim & Oral, Ece, 2011. "A robust alternative to the ratio estimator under non-normality," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 930-936, August.
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