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.
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