| dc.description.abstract | Statisticians use survey sampling methods in the estimation of population parameters of interest. This field has received increased demand due to the reliable statistic they produce. Information is extracted from the samples and used to make inferences about the population and used for
planning purposes. This information is collected either by survey sampling or census. However,
the census is an expensive and tedious method to carry out in the estimation process thus preferring survey sampling in estimation. In survey sampling, estimation can be either parametric or nonparametric. In the nonparametric, estimation of the finite population total divides into the sampled
and non-sampled parts. Estimation of the sampled part is quite easy thus the problem reduces to the estimation of the non-sampled part. Different approaches have been used by statisticians in the
estimation of the non-sampled part. These approaches have however relied on the use of kernel smoothers and have been known to suffer from the problem of boundary bias. In this study, a nonparametric estimator for a finite population total that addresses this drawback of kernel smoothers is proposed. The properties of this estimator were studied empirically in order to
determine its efficiency. The estimator was applied to simulated data and comparative analysis was done using R statistical software version i386 4.0.3 and the results of the bias were confirmed. The performance of the proposed estimator was tested and compared against the
design-based Horvitz-Thompson estimator, the model-based approach proposed by Dorfman, and the ratio estimator. The proposed estimator was developed by modifying the NadarayaWatson kernel estimator using two boundary bias-reducing techniques. The bias, variance, and
Mean Squared Error of the estimator were studied theoretically and applied to an empirical study
using simulated data from linear, quadratic, and exponential mean functions. Both the
unconditional and conditional properties of the estimators under the three mean functions were investigated. The proposed estimator outperformed the ratio estimator, Horvitz-Thompson estimator, and the estimator due to Dorfman in quadratic and exponential mean functions. This is evident from the small biases and means squared error values obtained. For the linear mean
function, the ratio estimator gave the best estimates because it is (BLUE). Therefore, the proposed nonparametric estimator for a finite population total was developed, the asymptotic properties were studied and comparative analysis was done using simulated data. From the results
obtained, the proposed estimator was found to give smaller biases and therefore can be
recommended for bias correction at the boundary. The proposed estimator in this study is based on stratified sampling, thus a study using cluster sampling is recommended to compare the performance of the estimator and further research to improve the estimator to work for all
theoretical data variables | en_US |
