Microsoft Corporation
UNIVARIATE DENSITY ESTIMATION METHOD

Abstract:

A method for use with a computing device. The method may include receiving a data set including a plurality of univariate data points and determining a target kernel bandwidth for a kernel density estimator (KDE). Determining the target kernel bandwidth may include computing a plurality of sample KDEs and selecting the target kernel bandwidth based on the sample KDEs. The method may further include computing the KDE for the data set using the target kernel bandwidth. For one or more tail regions of the data set, the method may further include computing one or more respective tail extensions. The method may further include computing and outputting a renormalized piecewise density estimator that, in each tail region, equals a renormalization of the respective tail extension for that tail region, and, outside the one or more tail regions, equals a renormalization of the KDE.