Estimation of Population Mean in the Presence of Non-Response for Time-Based Surveys

Abstract

An estimate of the location of a distribution is the most fundamental type of inference about a population. Consequently, obtaining more accurate estimators of the population mean of interest is essential in every statistical estimating technique. Survey statisticians most often use priori information at an estimation stage to form an estimator for estimating parameters. In this study, we suggested an estimator for the population mean in the presence of non-response utilizing information from the past surveys along with information available from the current surveys in the form of a hybrid exponentially weighted moving average. We obtained the expressions of the suggested estimator's mean and variance and established the mathematical conditions to demonstrate the efficiency of the suggested estimator. We supported the theoretical outcomes with the help of a simulation study and a real-life example. The results show that the utilization of information from past surveys along with the current surveys improves the efficiency of the suggested estimator. For example: in the simulation study, for a sample size n=(50, 100) at the non-response rate (=0.20, 0.15) and weights (0.10) and  (0.15) to the current and past observations, variances of the suggested estimator were  0.000683, 0.000559; 0.000635, 0.000309), which were less than (0.020944, 0.009756; 0.020024, 0.008920) of the existing Hansen and Hurwitz (1946) estimator. Similarly, in the empirical study of the real-life dataset, for the sample number (=6) having size n (=6) at (=0.30, 0.25), (=0.10) and   (=0.15), variances of the suggested estimator were (0.74, 0.71), which were significantly less than (95.12, 90.65) of the existing Hansen and Hurwitz (1946) estimator. The suggested work is limited to the homogeneous population only.