Accuracy of transformed kernel density estimates for a heavy-tailed distribution

Nonparametric estimation for the density of a heavy-tailed probability distribution is studied through transformation of initial observations. The accuracy of transformed kernel estimates with constant and variable window width in the sense of mean integrated squared error for different transformations is determined. Boundary kernel are designed for improving estimation on distribution tails. For a kernel estimate with variable window width, the mismatch method ensures a mean integrated squared estimation error close to the optimal error.