Iterated Transformation-Kernel Density Estimation
Lijian Yang, James Stephen Marron · Journal of the American Statistical Association · 1999
Transformation from a parametric family can improve the performance of kernel density estimation.In this paper, we give two data-driven estimators for the optimal transformation parameter.We demonstrate that multiple families of transformations can be employed at the same time, and there can be bene ts to iterating this process.The transformation scheme can be expected to rst pick the right transformation family and then the optimal parameter.Insight as to the performance of the method comes from our analysis of a number of real datasets, two of which are included in this paper.To illustrate the e ectiveness and asymptotics of the transformation method, we also present results on one of the ve target densities used in our simulation study.It is then proved that the Johnson Family of transformations, when coupled with transformation-kernel density estimation, makes a wide variety of density shapes easier to estimate.The transformation method has overall better performance than the usual method and in many cases it is much more e ective.