Improved the bias in kernel quantile function estimation

In this paper, a new estimator for kernel quantile estimation is given to reduce the bias. The asymptotic properties of the proposed estimator was established and it turned out that the bias has been reduced to the fourth power of the bandwidth, while the bias of the estimators considered has the second power of the bandwidth, while the variance remains at the same order. Futhermore, we calculate the optimal bandwidth which minimizes the asymptotic mean squared error. A simulation study and a real data example are carried out to illustrate the performance of the proposed estimator and compared with other existing approaches mentioned.