School of Mathematics Weekly Seminar

March 17, 1:00 pm

PhD Proposal Seminar


Modeling optimal estimators for population parameters has been an area of interest to many statisticians. Auxiliary variable that is highly correlated with the response variable can be used enhance performance of constructed estimators. Use of auxiliary variable(s) in estimation problems has called for the construction of ratio estimators. Efficiency of constructed ratio-type estimators is improved when more auxiliary variables are used in the survey problems. Asymptotic properties of constructed estimators are usually distorted by non-response in the study variable. Various corrective measures have been suggested in literature to take care of the non-response. Such solutions include, among others, imputation, partial deletion, resampling, weight adjustment and sub-sampling. In this study, we have constructed an unbiased ratio estimator for finite population total in stratified random sampling under non-response. This has been done under both univariate and multivariate ratio estimations. In univariate, we have considered separate and combined ratio estimations and regression forms of the constructed estimator. From the Percent Relative Efficiency (PRE) computations, we have observed that stratification improves performance of the constructed estimator by 10.26% compared to SRSWOR. We have also seen that the sub-sampling method adopted in this study improves efficiency of the constructed estimator by 0:44% if we were to use partial deletion to take care of non-response. Further, we have observed that the regression form of the suggested estimator performs better that the original estimator in SRSWOR (PRE = 100:00%) and in stratified random sampling, using both separate ratio (PRE = 110.26%) and combined ratio (PRE = 106.39%) estimation methods. From multivariate unbiased ratio estimation, we have considered a two dimensional auxiliary random vector and observed that performance of the constructed multivariate ratio estimators depends on the choice of multivariate weights. From simulation results, we recommend that further studies should be done on unbiased ratio estimation when non-response is in both response variable and auxiliary variable(s). Moreover, further studies should consider multivariate cases where the dimensionality of the auxiliary random vector is more than 2.

Key Areas: Unbiased Ratio Estimator, Stratified Random Sampling, Non-Response in Sample Surveys