Estimation of Finite Population Total in Presence of Missing Values in Two-Phase Sampling

Abstract

Missing data is a real problem in many surveys. To overcome the problems caused by missing data, partial deletion and single imputation methods among others have been proposed. However, problems such as discarding usable data, inaccuracy in reproducing known population parameters and standard errors are associated with them. In ratio, regression and stochastic imputation, it is assumed that there is a variable with complete cases that can be used as a predictor in estimating missing values in the other variable(s) and the relationship between the dependent and independent variable(s) is linear. This might not always be the case. To overcome these problems accompanied to stochastic and regression estimation, two-phase sampling and nonparametric model-based estimation were employed in this research. Estimator of population total in two-phase sampling was modified. The variance of estimator developed by Hidiroglou, Haziza and Rao was used to compare the performance of the proposed non-parametric model-based imputation in reproducing well known population total and standard errors compared to mean, regression and stochastic methods of imputation. The data was simulated and analyzed using R-statistical Software. The empirical study revealed that non-parametric model-base imputation method is better in reproducing both known population total and standard error.