Predictive Estimation of Finite Population Mean in Case of Missing Data Under Two-phase Sampling

The present paper deals with the problem of estimation of finite population mean of study variable using two auxiliary variables in two-phase sampling scheme using predictive approach in case of missing values of the study variable and unknown population mean of first auxiliary variable. Four classes of such estimators have been proposed using this predictive approach. The expressions of bias and mean square errors are derived up to first order of approximation. The optimal values of the constants involved in the proposed classes of estimators have been obtained and thus minimum mean square errors of the proposed classes are obtained in this study. The empirical and graphical comparisons with regression type estimators (under single phase and double phase sampling scheme) and also among themselves have been made for evaluating the performance of the proposed classes for different choices of non-responding units. Five real data sets and three simulated data sets following normal distribution have been used to evaluate the performance of the proposed classes. Numerical findings confirm the theoretical results obtained regarding superiority of proposed classes of estimators over the conventional regression type estimators in terms of percent relative efficiencies.

Automated summary

This paper addresses the problem of estimating the finite population mean using two auxiliary variables and a predictive approach in a two-phase sampling scheme, particularly in the presence of missing values and unknown population mean. Four classes of estimators are proposed based on this predictive approach. The expressions for bias and mean square errors are derived up to the first order of approximation. Optimal values of the involved constants are obtained to obtain the minimum mean square errors. The performance of the proposed estimators is evaluated through empirical and graphical comparisons with regression type estimators, both under single phase and double phase sampling schemes. Real and simulated data sets are used to validate the theoretical results, demonstrating the superiority of the proposed estimators in terms of percent relative efficiencies.