A Simulation Study of a General Class of Direct Estimator for Mean of Domain using Imputation Technique
摘要
Missing data occurring due to non-response is a common problem in the estimation of small area. It poses a significant challenge for domain estimation as it introduces bias and increases variability, making it crucial to adopt an appropriate imputation method. Bhushan et al. (Sankhya B:1–52, 2024a) have proposed general class of imputation methods for domain mean estimation. The main objective behind the formulation of the proposed imputation method is to obtain an estimator having less mean square error (MSE) and higher precision than the existing estimators, suggested by Bhushan et al. (Sankhya B:1–52, 2024a). Keeping this in consideration, we have suggested a general class of direct estimator for estimating the mean of domain in missing data based on imputation technique under simple random sampling without replacement (SRSWOR). The bias and MSE of the proposed estimator are obtained upto the first order of approximation. Some of the estimators discussed by Bhushan et al. (Sankhya B:1–52, 2024a) are found as the members of the suggested estimator. The suggested general class of direct estimator outperforms under the derived mathematical conditions. It is then verified with the help of empirical study using an authentic dataset MU284. Also, simulation analysis based on hypothetical dataset is done using R programming language to further justify the results. The confidence intervals for MSEs of the estimators are calculated for 95% confidence level. The empirical and simulation findings demonstrate that the proposed estimator consistently outperforms the existing estimators in terms of lower MSE and higher precision.