A General Class of Estimators of the Population Mean in Survey Sampling Using Auxiliary Information with Sub Sampling the Non-Respondents

In this paper we have considered the problem of estimating the population mean $\bar{Y}$ of the study variable y using auxiliary information in presence of non-response. Classes of estimators for $\bar{Y}$ in the presence of non-response on the study variable y only and complete response on the auxiliary variable x is available, have been proposed in different situations viz., (i) population mean $\bar{X}$ is known, (ii) when population mean $\bar{X}$ and variance $S^2_x$ are known; (iii) when population mean $\bar{X}$ is not known: and (iv) when both population mean $\bar{X}$ and variance $S^2_x$ are not known: single and two-phase (or double) sampling. It has been shown that various estimators including usual unbiased estimator and the estimators reported by Rao (1986), Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) are members of the proposed classes of estimators. The optimum values of the first phase sample size n', second phase sample size n and the sub sampling fraction 1/k have been obtained for the fixed cost and the fixed precision. To illustrate foregoing, we have carried out an empirical investigation to reflect the relative performance of all the potentially competing estimators including the one due to Hansen and Hurwitz (1946) estimator, Rao (1986) estimator, Khare and Srivastava (1993, 1995) and Tabasum and Khan (2006) estimator.