Random weighing approximation for continuous empirical process

For estimation of empirical process in data analysis, Kolmogorov statistics is traditionally used. This paper presents a new estimation-random weighing approximation for continuous empirical process. Firstly, a core function method was employed to construct a smooth empirical distribution function for an unknown sample distribution. Then, a random weighing approximation was defined for continuous empirical process. Finally, because Brown Bridge's sample function was continuous, the approximation consistent was proved under suitable conditions. The computer simulation showed that the new methods were effective.