Higher-order bias corrections for kernel type density estimators on the unit or semi-infinite interval

For the data of size n from the unit or semi-infinite interval, several asymmetric kernel density estimators, having the mean integrated squared errors of order $O\left(n^{-4/5}\right)$ or $O\left(n^{-8/9}\right)$, are available in the literature. We develop more higher-order bias-corrected estimators, achieving the order $O\left(n^{-4p/(4p+1)}\right)$, where $p\ge 2$ is a given integer. We illustrate the finite sample performance of the estimators through the simulations.