Estimation of the Population Mean for Incomplete Data by using Information of Simple Linear Relationship Model in Data Set

Abstract

The objective of this research is to propose the estimator of the population mean for incomplete data by using information of simple linear relationship model in the data set.In addition, the factorization of the likelihood function is created to derive the maximum likelihood estimator for the population mean.The simulation study was conducted for 630 situations to compare the efficiency of the proposed estimator with the two population mean estimators, namely pairwise deletion and Anderson estimators.In this study, two criteriabias and mean square error-of the performances for estimators are examined.It is found that all percentage levels of missing data, the mean square error of the proposed estimator tends to be lower than those of pairwise deletion and Anderson estimators for the large correlation levels between two variables in the data set whatever the sample sizes will be, especially for the large percentage level of missing data.However, for the small correlation between two variables in the data set, the three estimators tend to have the same performances in terms of both two criteria for all sample sizes and all percentage levels of missing data.