Adapted Exponential Type Estimator in the Presence of Non-response
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.
Hansen, M. H., and Hurwitz, W. N. (1946). The problem of non-response in sample surveys, Journal of the American Statistical Association, 41(236), 517–529.
Cochran, W.G., Sampling Techniques, John Wiley and sons, New-York, 1977.
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.