Homogeneous Imputation under Two Phase Probability Proportional to Size Sampling

In this paper, we consider the problem of missing complete at random (MCAR) values in two-phase probability proportional to size ( pps) sampling for the estimation of population mean. For comprehensive examination of missing values, we discuss four possible situations for the occurrence of non-response. A class of estimators is considered by using an unknown constant with the traditional estimators for imputing the missing values. Theoretically, bias and mean squared errors of the proposed estimators are obtained up to the first order approximation. Two numerical studies are carried out for the relative comparison of the proposed estimators with mean estimator under two-phase ppssampling for each of the predefined situation.