IDEAS home Printed from https://ideas.repec.org/a/spr/aodasc/v8y2021i4d10.1007_s40745-020-00258-0.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40745-020-00258-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40745-020-00258-0?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 search for a different version of it.

    References listed on IDEAS

    as
    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.
    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. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    2. Mohammad Jafari Jozani & Saeed Majidi & François Perron, 2012. "Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling," Statistical Papers, Springer, vol. 53(3), pages 719-737, August.
    3. Jingli Lu, 2013. "The Chain Ratio Estimator and Regression Estimator with Linear Combination of Two Auxiliary Variables," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-4, November.
    4. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    5. Shashi Bhushan & Anoop Kumar, 2022. "Novel Log Type Class Of Estimators Under Ranked Set Sampling," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 421-447, May.
    6. V.L. Mandowara & Nitu Mehta (Ranka), 2012. "A better estimator of population mean with power transformation based on ranked set sampling," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(3), pages 551-558, December.
    7. Mariano Ruiz Espejo & Miguel Delgado Pineda & Saralees Nadarajah, 2013. "Optimal unbiased estimation of some population central moments," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 39-62, June.
    8. M. Mahdizadeh & Ehsan Zamanzade, 2022. "New insights on goodness-of-fit tests for ranked set samples," Statistical Papers, Springer, vol. 63(6), pages 1777-1799, December.
    9. A. Hussein & H. Muttlak & E. Al-Sawi, 2013. "Group sequential methods based on ranked set samples," Statistical Papers, Springer, vol. 54(3), pages 547-562, August.
    10. M. Mahdizadeh & Ehsan Zamanzade, 2020. "Estimation of a symmetric distribution function in multistage ranked set sampling," Statistical Papers, Springer, vol. 61(2), pages 851-867, April.
    11. Ehsan Zamanzade & Michael Vock, 2018. "Some nonparametric tests of perfect judgment ranking for judgment post stratification," Statistical Papers, Springer, vol. 59(3), pages 1085-1100, September.
    12. Shashi Bhushan & Anoop Kumar & Sana Shahab & Showkat Ahmad Lone & Salemah A. Almutlak, 2022. "Modified Class of Estimators Using Ranked Set Sampling," Mathematics, MDPI, vol. 10(21), pages 1-13, October.

    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:spr:aodasc:v:8:y:2021:i:4:d:10.1007_s40745-020-00258-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.