Mobius-Like Mappings and Their Use in Kernel Density Estimation

Abstract

It is well known that the manipulation of sample data by means of a parametric function can improve the performance of kernel density estimation. This article proposes a two-parameter Mobius-like function to map sample data drawn from a semi-infinite space into [−1,1). A standard kernel method is then used to estimate the density. The proposed method is shown to yield effective estimates of density and is computationally more efficient than other well-known transformation methods. The efficacy of the technique is demonstrated in a practical setting by application to two datasets.