Gram-Charlier A Series Based Extended Rule-of-Thumb for Bandwidth Selection in Univariate Kernel Density Estimation

Bandwidth parameter estimation in univariate Kernel Density Estimation has traditionally two approaches. Rule(s)-of-Thumb (ROT) achieve ‘quick and dirty’ estimations with some specific assumption for an unknown density. More accurate solve-the-equation-plug-in (STEPI) rules have almost no direct the density but demand high computation. This article derives a balancing third approach. Extending of Gaussianity to be estimated \textit{normal reference} ROT (NRROT) near Gaussianity, then expressing using Gram-Charlier A (GCA) series minimize asymptotic mean integrated square error, it GCA based Extended (GCAExROT). The performance analysis simulated real datasets suggests replace NRROT by modified GCAExROT rule achieving accuracy nearer STEPI at computation NRROT, specifically small samples.