Estimation of Population Mean Using Imputation Techniques in Sample Survey Under Two-Phase Sampling Scheme

A sample survey remains incomplete in presence of missing data and 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 Ratio method of imputation, Compromised method of imputation, Mean method of imputation, Ahmed method of imputation, F-T method of imputation, and so on. These suggested methods are based on either population parameter of auxiliary variable or available information (both study and auxiliary variable) in the sample. 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 exponential dual to ratio type imputation methods for missing values in two phase sampling. Two different sampling designs in two-phase sampling are compared under imputed data. The Bias and M.S.E. of suggested estimators are derived in the form of population parameters using the concept of large sample approximation. Numerical study is performed over two populations using the expressions of Bias and M.S.E. and efficiency compared with existing estimators.