Mean Integrated Squared Error of Kernel Estimators when the Density and Its Derivative Are Not Necessarily Continuous

摘要

The asymptotic behavior of the mean integrated squared error (MISE), the optimal value of MISE, the asymptotically minimum value of MISE, and the optimal kernel of a density function f of a finite number of random variables identically distributed, when f and its derivative are not necessarily continuous, are studied. Rosenblatt-Epanechinkov's results are extended to the case where the density function is not continuous.