Variance Estimation in Two Phase Sampling in Presence of Non Response

Abstract

The variability in a process or estimate is of importance in almost all areas of life. The statistical measure to obtain variability in a process or estimate is the variance. The variance also appears as a parameter in well-known Gaussian distribution that is considered as a corner-stone in many statistical analyses. Variance provides an insight into average squared spread in the data from the mean. In the study of process control, a process with least spread is preferred as the process will provide products that have least variability from underlying specifications. In practice, the variance of a process is estimated by using the sample data and various methods are available to do the same. In this research we have proposed some efficient methods to estimate the spread of the data in single phase sampling by using single transformed auxiliary variable. The Mean Square Errors (MSE) of the proposed estimators have been obtained. The performance of the proposed estimator has been studied by using numerical as well as simulation studies. Some special cases of the new proposed estimator have been listed. An estimator of population variance using two transformed auxiliary variables has also been suggested. The Mean Square Error of the proposed estimator, up to first order of approximation, has been obtained. The numerical and simulation studies have been carried out to study the performance of the proposed estimator. Estimators of the population variance have been derived under two situations of non response in two phase sampling. The properties of the proposed methods were studied by conducting the numerical as well as simulation studies. The study has been conducted by using some special cases of the proposed estimator and some existing estimator. It has been found that our proposed estimators perform better as compared with the existing estimators as they have smaller mean square error in numerical as well as in simulation studies