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.
Mugdadi, Abdel-Razzaq and Sani, Rugayyah
The Linear Combination of Kernels in the Estimation Of Cumulative Distribution Functions,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 9.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/9