Estimating a finite population mean under random non-response in two-stage cluster sampling with replacement - Bii, Nelson Kiprono (Strathmore University, 2020)
Non-response is a regular occurrence in sample surveys. Developing estimators when non-response exists may result in large biases when estimating population parameters. In this study, a finite population means estimator has been developed under two-stage cluster sampling with replacement in the presence of random non-response. It is assumed that non-response arises in the survey variable in the second stage of cluster sampling assuming full auxiliary information is known. A weighting method of compensating for non-response has been applied. Kernel density estimation was used and the modified transformation of data method was incorporated in order to address the boundary effects due to the Nadaraya-Watson estimator used in the estimation process. Asymptotic properties of the proposed estimator of the finite population mean have been derived. The performance of the proposed estimator has been compared with other estimators based on bias, mean squared error, and confidence interval lengths using simulated data. The results revealed that the estimator proposed has smaller mean squared error values and shorter confidence interval lengths when compared to other estimators of the finite population mean. The bias results also indicated that the proposed estimator of finite population means performed better than the Nadaraya-Watson and the improved Nadaraya-Watson estimators. The transformed estimator proposed to address boundary bias due to Nadaraya-Watson has also been shown to have smaller values of the bias, smaller mean squared error values, and shorter confidence interval lengths compared to those of the Nadaraya-Watson estimator. The results obtained can be useful in choosing efficient estimators of finite population mean for instance in demographic health sample surveys.
Submitted in total fulfillment of the requirements for the Degree of Doctor of Philosophy in Mathematical Statistics of Strathmore University