Multivariate Density Estimation Using Dimension Reducing Information and Tail Flattening Transformations

Abstract

We propose a nonparametric multiplicative bias corrected transformation estimator designed for heavy tailed data. The multiplicative correction is based on prior knowledge and has a dimension reducing effect at the same time as the original dimension of the estimation problem is retained. Adding a tail-flattening transformation improves the estimation significantly – particularly in the tail – and provides significant graphical advantages by allowing the density estimation to be visualized in a simple way. The combined method is demonstrated on a fire insurance data set and where it provides excellent performance in a data-driven simulation study.

Keywords: Bias reduction, Kernel, Multiplicative correction

JEL Classification: C14