Author(s)

Nicholas Makumi¹, Romanus Odhiambo Otieno², George Otieno Orwa³, Festus Were³, Habineza Alexis¹

¹Pan African University, Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya.
²Department of Mathematics, Meru University of Science and Technology, Meru, Kenya.
³Department of Statistics and Actuarial Sciences, JKUAT, Nairobi, Kenya.

In this paper, the problem of nonparametric estimation of finite population quantile function using multiplicative bias correction technique is considered. A robust estimator of the finite population quantile function based on multiplicative bias correction is derived with the aid of a super population model. Most studies have concentrated on kernel smoothers in the estimation of regression functions. This technique has also been applied to various methods of non-parametric estimation of the finite population quantile already under review. A major problem with the use of nonparametric kernel-based regression over a finite interval, such as the estimation of finite population quantities, is bias at boundary points. By correcting the boundary problems associated with previous model-based estimators, the multiplicative bias corrected estimator produced better results in estimating the finite population quantile function. Furthermore, the asymptotic behavior of the proposed estimators is presented. It is observed that the estimator is asymptotically unbiased and statistically consistent when certain conditions are satisfied. The simulation results show that the suggested estimator is quite well in terms of relative bias, mean squared error, and relative root mean error. As a result, the multiplicative bias corrected estimator is strongly suggested for survey sampling estimation of the finite population quantile function.

Quantile Function, Kernel Estimator, Multiplicative Bias Correction Technique, Simple Random Sampling without Replacement

Makumi, N. , Otieno, R. , Orwa, G. , Were, F. and Alexis, H. (2021) Bias Correction Technique for Estimating Quantiles of Finite Populations under Simple Random Sampling without Replacement. Open Journal of Statistics, 11, 854-869. doi: 10.4236/ojs.2021.115050.