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Generalized Exponential-Type Estimators for Population Mean Taking Two Auxiliary Variables for Unknown Means in Stratified Sampling with Sub-sampling the Non-Respondents

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Abstract

In this paper, we have considered stratified two-phase sampling design with sub-sampling the non-respondents in the presence of non-response for estimating population mean considering the information of two auxiliary variables. The proposed estimators are the exponential function of two auxiliary variables when means of the two auxiliary variables are not known in prior. Further the proposed estimators are provided with their generalized form. The bias and mean square error expressions of the proposed estimators have been derived in two different cases of non-response. The conditions for which proposed estimators are more efficient as compared to some other estimators, have also been discussed in each case of non-response. It is shown that the proposed estimators are more efficient as compared to Hansen and Hurwitz (J Am Stat Assoc 41:517–529, 1946) unbiased estimator and Tabasum and Khan (Assam Stat Rev 20(1):73–83, 2006) two-phase ratio and product estimators modified to the stratified sampling. An empirical study has also been carried out to demonstrate the performances of the estimators.

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Author information

Authors and Affiliations

  1. Department of Statistics, COMSATS Institute of Information Technology, Lahore, Pakistan

    Aamir Sanaullah & Muhammad Noor ul Amin

  2. Department of Statistics, National College of Business Administration and Economics, Lahore, Pakistan

    Muhammad Hanif

  3. Department of Statistics, Hacettepe University, Beytepe, Ankara, Turkey

    Nursel Koyuncu

Authors
  1. Aamir Sanaullah
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  2. Muhammad Noor ul Amin
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  3. Muhammad Hanif
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  4. Nursel Koyuncu
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Corresponding author

Correspondence to Nursel Koyuncu.

Appendix

Appendix

See Tables 5, 6 7 8 and 9.

Table 5 Percent relative efficiencies (PREs) of estimators with respect to \(\bar{{y}}_{st}^*\) for Case-I of non-response
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Table 6 Percent relative efficiencies (PREs) of estimators with respect to \(\bar{{y}}_{st}^*\) for Case-II of non-response
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Table 7 Data statistics
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Table 8 Data statistics
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Table 9 Data statistics
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Sanaullah, A., Noor ul Amin, M., Hanif, M. et al. Generalized Exponential-Type Estimators for Population Mean Taking Two Auxiliary Variables for Unknown Means in Stratified Sampling with Sub-sampling the Non-Respondents. Int. J. Appl. Comput. Math 4, 56 (2018). https://doi.org/10.1007/s40819-018-0489-7

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  • DOI: https://doi.org/10.1007/s40819-018-0489-7

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