Memory-type Mean Estimators for Surveys with Non-response: A Regression-imputation and Ewma Approach

Abstract

Sampling survey mostly faces the challenge of missing information or non-response, Missing data naturally occurs in sample surveys when a few sampling units refuse to respond or are unable to participate in the survey. In time based survey, this could happen due to relocation or system malfunctioning after some period. This missing information can bring about a substantial amount of bias, make the handling and analysis of the data more arduous and create reductions in efficiency of the estimator. Surmounting this challenge bring about the development of various imputation-based mean estimation methods. Some of these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent researches has changed this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This new invented methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present regression- imputation and EWMA based memory-type mean estimators in the presence of non- response. For the performance assessment between existing and proposed estimators, two real-life time-scaled data sets are considered. In the first data set proposed estimators (Tp1 and Tp2) have the minimum MSE and higher PRE and also in the second data set, results show that the proposed estimators (estimators (Tp1 and Tp2) have the minimum MSE and higher PRE when compared with the existing estimators at all levels of smoothing parameter. Therefore the proposed estimator will perform better in estimating the EWMA-based mean in the presence non response for time based survey and longitudinal survey. Most especially in quality control data that are collected over time. The current work is limited to simple random sampling which assumes homogeneity of the population units. Further work can be done on stratify random sampling which assumes heterogeneity of the population units.