Physical Sciences and Mathematics Commons^™

The Linear Combination Of Kernels In The Estimation Of Cumulative Distribution Functions, Abdel-Razzaq Mugdadi, Rugayyah Sani

Applications and Applied Mathematics: An International Journal (AAM)

The kernel distribution function estimator method is the most popular nonparametric method to estimate the cumulative distribution function F(x). In this investigation, we propose a new estimator for F(x) based on a linear combination of kernels. The mean integrated squared error, asymptotic mean integrated squared error and the asymptotically optimal bandwidth for the new estimator are derived. Also, based on the plug-in technique in density estimation, we propose a data based method to select the bandwidth for the new estimator. In addition, we evaluate the new estimator using simulations and real life data.