  In recent years, kernel density estimation has been exploited by computer
scientists to model machine learning problems. The kernel density estimation
based approaches are of interest due to the low time complexity of either O(n)
or O(n*log(n)) for constructing a classifier, where n is the number of sampling
instances. Concerning design of kernel density estimators, one essential issue
is how fast the pointwise mean square error (MSE) and/or the integrated mean
square error (IMSE) diminish as the number of sampling instances increases. In
this article, it is shown that with the proposed kernel function it is feasible
to make the pointwise MSE of the density estimator converge at O(n^-2/3)
regardless of the dimension of the vector space, provided that the probability
density function at the point of interest meets certain conditions.
