Ratio Estimation of Finite Population Total in Stratified Random Sampling Under Non-response
Abstract
Estimation of population parameters has been an area of interest to many
statisticians. Auxiliary variable that is highly correlated with the response
variable can be used to improve efficiency of constructed estimators. Efficiency
of constructed estimators is improved when more auxiliary variables
are used in the survey problems. However, asymptotic properties of constructed
estimators are usually interfered with by non-response in the study
variable. Various corrective measures, such as imputation, partial deletion,
resampling, weight adjustment and sub-sampling, have been suggested in
literature to take care of the non-response. In this study, we have adopted
the sub-sampling approach to construct a 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
case, 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 simple
random sampling without replacement. Also, the sub-sampling method
adopted improved efficiency of the constructed estimator by 0:44% when
partial deletion is used. From multivariate unbiased ratio estimation, a two
dimensional auxiliary random vector was constructed and it was observed
that performance of the constructed multivariate ratio estimators depends on
the choice of multivariate weights. This study has shown how an unbiased
ratio estimator for finite population total is constructed in stratified random
sampling. The study has also shown how the problem of non-response in
sample surveys can be corrected using sub-sampling method.
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Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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