Abstract:

In consideration of  the probability density estimation problem with surrogate  and validation data, a recursive kernel estimation of probability density function is so defined to comprise both surrogate  and validation variates that the proposed estimators are proved to be asymptotically normal. The  simulation results indicate at a given constant of N, the total number of data, the method performs better as the validation variate n increases. Also, for a given n, simulation result becomes better in terms of top as N increases, but becomes bad in terms of tail. We also noted that the simulation result, as N and n together increases, more approaches the f(x) and is smoothing.

Key words: recursive kernel estimation, asymptotically normal, kernel function