Volume 3, Issue 5, October 2015, Page: 214-224
Spline Regression in the Estimation of the Finite Population Total
Joseph Kipyegon Cheruiyot, Department of Computer and Statistics, Moi University, Eldoret, Kenya
Received: Aug. 10, 2015;       Accepted: Aug. 20, 2015;       Published: Sep. 2, 2015
DOI: 10.11648/j.sjams.20150305.11      View  3523      Downloads  101
Abstract
This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.
Keywords
Homoscedasticity, Population, Sample, Spline Regression, Robustness, Smoothing, Estimator
To cite this article
Joseph Kipyegon Cheruiyot, Spline Regression in the Estimation of the Finite Population Total, Science Journal of Applied Mathematics and Statistics. Vol. 3, No. 5, 2015, pp. 214-224. doi: 10.11648/j.sjams.20150305.11
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