Adapted Exponential Type Estimator in the Presence of Non-response

  • Ceren Ünal Department of Statistics, Hacettepe University, 06800 Beytepe, Ankara, Turkey
  • Cem Kadilar Department of Statistics, Hacettepe University, 06800 Beytepe, Ankara, Turkey
Keywords: Exponential Type Estimator, Auxiliary Variable, Non-Response, Population Mean, Efficiency.

Abstract

In this article, we propose an estimator using the exponential function for the population mean in the case of non-response on both the study and the auxiliary variables. The equations for the Bias and Mean Square Error (MSE) are derived to the first order of approximation and theoretical comparisons are made with existing estimators in literature. Besides, we examine the efficiency of the proposed estimator according to the classical ratio and regression estimator, Hansen-Hurwitz unbiased estimator, and the estimator of Singh et al. (2009). Following theoretical comparisons, we infer that the proposed estimator is more efficient than compared estimators under the obtained conditions in theory. Moreover, these theoretical results are supported numerically by providing an empirical study on five different data sets.

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Author Biographies

Ceren Ünal, Department of Statistics, Hacettepe University, 06800 Beytepe, Ankara, Turkey

Ceren Ünal received her B.Sc. and M.Sc. degrees in Statistics from Hacettepe University, Turkey, in 2014 and 2017. She is a Ph.D. student at the same university. She is currently working as a research assistant in the Department of Statistics at Hacettepe University. Her research interest is Sampling.

Cem Kadilar, Department of Statistics, Hacettepe University, 06800 Beytepe, Ankara, Turkey

Cem Kadilar was born in Ankara in Turkey in 1972. After graduation from higher school Ankara College, he received his B.Sc., M.Sc., and Ph.D. degrees in Statistics from Hacettepe University. He became Associate Professor in 2004 and Professor in 2010 at the same university. He has approximately 150 publications and more than 3500 citations. His interest areas are Sampling, Time Series Analysis, and Survival Analysis.

References

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Singh, R., Kumar, M., Chaudhary, M. K., and Smarandache, F. (2009). Estimation of mean in presence of non-response using exponential estimator. arXiv preprint arXiv:0906.2462.

Vishwakarma, G. K., Singh, R., Gupta, P. C., and Pareek, S. (2016). Improved ratio and product type estimators of finite population mean in simple random sampling, Investigación Operacional, 37(1), 70–76.

Khare, B. B., and Kumar, S. (2009). Utilization of coefficient of variation in the estimation of population mean using auxiliary character in the presence of non-response, National Academy Science Letters-India, 32(7–8), 235–241.

Khare, B. B., and Sinha, R. R. (2009). On class of estimators for population mean using multi-auxiliary characters in the presence of non-response, Statistics in Transition, 10(1), 3–14.

Khare, B. B., and Srivastava, S. (1993). Estimation of population mean using auxiliary character in presence of non-response, National Academy Science Letters, 16, 111–111.

Sinha, R. R., and Kumar, V. (2015a). Estimation of mean using double sampling the non-respondents with known and unknown variance, International Journal of Computing Science and Mathematics, 6(5), 442–458.

Sinha, R. R., and Kumar, V. (2015b). Families of estimators for finite population variance using auxiliary character under double sampling the non-respondents, National Academy Science Letters, 38(6), 501–505.

Published
2021-06-30
Section
Articles