The problem of nonparametric estimation of a univariate density with rth continuous derivative on compact support is addressed (r≥2). If the density function has compact support and is non-zero at either boundary, regular kernel estimator will be completely biased at such boundary. Although several correction methods were proposed to improve the bias at the boundary to h2 in the last decades, this paper initiates a way to further improve bias to higher order (hr) for...