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A comparative study of a class of direct estimators for domain mean with a direct ratio estimator for domain mean using auxiliary character

Author

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  • Khare Brij Behari

    (Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India)

  • Ashutosh

    (Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India)

  • Rai Piyush Kant

    (Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India)

Abstract

Estimation techniques for a domain parameter play a very significant role in the theory of sample surveys. In the recent years many advanced methodologies have been developed for domain estimation. In particular, direct and synthetic estimators are applied for the estimation of domain mean in the government and private sectors under certain assumptions as to the size of the samples relating to particular domains. The findings demonstrate that the direct estimator fails to perform more efficiently as compared to the synthetic estimator when reliable units are not directly accessible in the studied domains. Moreover, due to the fact that small units belong to the sample of the studied domain, the direct estimator produces an unacceptably large standard error. In contrast, if a sufficient number of units are available in the studied domain, the direct estimator produces effective results. This paper presents the theoretical aspects of the proposed class of direct estimators for domain mean with the use of a single auxiliary character, compared with an existing direct ratio estimator for domain mean (given in section 3.2). In addition, an empirical study has been provided to support the validity of the proposed estimators. The findings prove that the proposed estimators outperform the direct ratio estimator for domain mean using a single auxiliary character in the case of two studied populations and their analysed domains considered from Sarndal et al. (1992).

Suggested Citation

  • Khare Brij Behari & Ashutosh & Rai Piyush Kant, 2021. "A comparative study of a class of direct estimators for domain mean with a direct ratio estimator for domain mean using auxiliary character," Statistics in Transition New Series, Polish Statistical Association, vol. 22(2), pages 189-200, June.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:2:p:189-200:n:9
    DOI: 10.21307/stattrans-2021-023
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    References listed on IDEAS

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    1. S. Srivastava, 1983. "Predictive estimation of finite population mean using product estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 30(1), pages 93-99, December.
    2. K. K. Pandey & P. K. Rai, 2013. "Synthetic estimators using auxiliary information in small domains," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 14(1), pages 31-44, March.
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