Improvement of the method of kernel estimation by local polynomial approximation of the empirical distribution function and its application to empirical regression.

The kernel estimation of an unknown density function derived from measured values has at least one disadvantage: the second central moment of the estimated density is greater than the sample variance. This is unsatisfactory. It is possible to reduce the difference between both variances by an improvement of the method of kernel estimation. But for improved GAUSS-kernels it is not possible to reduce it to zero.