Abstract
The main objective of this study is to investigate the relative performance of donor imputation method in situations that are likely to occur in practice and to carry out numerical comparative study of estimators of variance using Nadaraya-Watson kernel estimators and other estimators. Nadaraya-Watson kernel estimator can be viewed as a non-parametric imputation method as it leads to an imputed estimator with negligible bias without requiring the specification of a parametric imputation model. Simulation studies were carried out to investigate the performance of Nadaraya-Watson kernel estimators in terms of variance. From the results, it was found out that Nadaraya-Watson kernel estimator has negligible bias and its variance is small. When compared with Naïve, Jackknife and Bootstrap estimators, Nadaraya-Watson kernel estimator was found to perform better than bootstrap estimator in linear and non-linear populations.
Highlights
Donor imputation is a method in which the missing values for one or more variables of a non responding unit are replaced by the corresponding values of a responding unit with no missing value for these variables
Donor imputation may not be the most efficient method in any specific scenario, it is popular in surveys due to its practical advantages
Some methods of variance estimation that have been developed for use with imputed data include a modelassisted method [11], an adjusted jackknife method [11], and multiple imputations [8]. [2] considered Random HotDeck (RHD) imputation under more general sampling designs assuming a one-factor analysis of variance model holds. [9], [6] and [5] dealt with Nearest Neighbor Imputation (NNI). [3] considered NNI, an alternative to resampling variance estimation method. [10] considered NNI under simple random sampling assuming that a ratio imputation model holds. [1] dealt with general donor imputation methods including NNI and with possibly postimputation edit rules and hierarchical imputation classes, under general sampling designs and more general imputation models
Summary
Donor imputation is a method in which the missing values for one or more variables of a non responding unit (recipient) are replaced by the corresponding values of a responding unit (donor) with no missing value for these variables. It is a variance estimation method which is valid even in the presence of high sampling fractions [1]. [2] considered Random HotDeck (RHD) imputation under more general sampling designs assuming a one-factor analysis of variance model holds. [10] considered NNI under simple random sampling assuming that a ratio imputation model holds. Non-parametric variance estimation using donor imputation method have been considered with estimation of parametersand being done using the kernel method proposed by Nadaraya (1964) and Watson (1964)
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