Estimation of Mean under Imputation of Missing Data using Exponential-Type Estimators in Two-Phase Sampling

To estimate the population mean with imputation i.e, the technique of substituting missing data, there are a number of techniques available in literature like mean method, ratio method, compromised method and so on. If population mean of auxiliary information is unknown then these methods are not useful and the two–phase sampling is used to obtain the population mean. This paper presents some imputation methods for missing values in two phase sampling .Two different sampling designs in two phase sampling is compared under imputed data. The PRE and MSE of suggested estimators are derived in the form of population parameters using the concept of large sample approximations. Numerical study is performed over empirical population in order to compare the performance of the suggested sampling designs using the expression over PRE and MSE .