Abstract
The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.
Highlights
Longitudinal surveys refer to a type of sampling surveys done repeatedly over time on the same sampled units
In terms of the percentage relative bias (%RB), at time point t = 2, it can be seen that the local linear estimator has the least value followed by the Nadaraya-Watson estimator and the simple linear regression estimator, which was the largest value of %RB
At time point t = 4, observe that the local linear estimator has the least %RB value followed by the simple linear regression estimator and the Nadaraya-Watson estimator performed worst
Summary
Longitudinal surveys refer to a type of sampling surveys done repeatedly over time on the same sampled units. While longitudinal surveys are regarded to be better and reliable in informing about various features of a study unit, they suffer from monotone and intermittent patterns of missing data. Nadaraya-Watson technique of [3] and [4] used in the imputation of missing values in the longitudinal data has some weaknesses of producing a large design bias and boundary effects that give unreliable estimates for inference. As shown by [5] and [6], a rival for Nadaraya-Watson technique is the local linear regression estimator which was found to produce unbiased estimates without boundary effects. In order to overcome the limitations of Nadaraya-Watson estimator, we derive a local linear regression estimator in the imputation of the nonresponndents in a longitudinal data set. A simulation study is conducted to determine the best performing estimator of the finite population mean
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