A bias reducing technique in kernel distribution function estimation

In this paper we suggest a bias reducing technique in kerneldistribution function estimation. In fact, it uses a convex combination of three kernel estimators, and it turned out that the bias has been reduced to the fourth power of the bandwidth, while the bias of the kernel distribution function estimator has the second power of the bandwidth. Also, the variance of the proposed estimator remains at the same order as the kernel distribution function estimator. Numerical results based on simulation studies show this phenomenon, too.