New Product Estimators for Population Mean Under Unequal Probability Sampling with Missing Data: A Case Study on the Number of New COVID-19 Patients

Abstract

The coronavirus pandemic or COVID-19 has killed numerous human lives and the number of COVID-19 patients all over the world including Thailand has drastically increased. Estimating the incidence of COVID-19 can assist in preventing further impacts through policies and planning for the whole nation. Although some information about COVID-19 are missing. If analysis is conducted without dealing with the issue, imprecise estimations may be made from the data. New product estimators along with the variance estimators for estimating population mean have been introduced  under unequal probability sampling without replacement with missing data in the study variable under two nonresponse mechansims; missing completely at random and missing at random. Two frameworks are considered;  the two-phase and reverse frameworks to find the variance estimators. Simulation studies and an application to COVID-19 patients investigate the performance of the proposed estimators. The results show that the proposed estimators under the missing at random nonresponse mechanism performs the best with the smallest variance compared to other estimators under both frameworks with the estimated mean of new COVID-19 patients equal to 306 cases per week.