Improved estimation of finite population median under two-phase sampling when using two auxiliary variables

Abstract

We propose an efficient estimator for population median under two-phase sampling when using two auxiliary variables on the lines of Diana [Diana, G. “A class of estimators of the population mean in stratified random sampling”, Statistica, 1, pp. 59-66 (1993)] and Jhajj and Walia [Jhajj, H. S. and Walia, G. S. “A generalized difference-cum-ratio type estimator for the population variance in double sampling”, Communications in Statistics-Simulations and Computation, 41, 58-64. (2012)]. The expressions for mean squared errors are presented, correct to first order of approximation. Both theoretical and numerical comparisons reveal that the proposed estimator performs better than the unbiased sample median estimator, ratio estimator, and estimators by Srivastava et al. [Srivastava, S. K., Rani, S., Khare, B. B., and Srivastava, S. R. “A generalized chain ratio estimator for mean of finite population”, Journal of the Indian Society of Agricultural Statistics, 42(1), pp. 108-117 (1990)] and Gupta et al. [Gupta, S., Shabbir, J., Ahmad, S. “Estimation of median in two phase sampling using two auxiliary variables”, Communications in Statistics-Theory and Methods, 37(11), pp. 1815−1822 (2008)].