Data-Driven Smoothing Parameter Selection in Density Estimation

• Activity Number: 387 - Software
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Sachithra Gangadari Rathnayake Opathalage* and Alexandre Leblanc
• Companies: University of Manitoba - Winnipeg, MB and University of Manitoba - Winnipeg, MB
• Keywords: Kernel density estimation; Nonparametric density estimation; Bandwidth selection; Bernstein density estimation; Order selection; Bootstrapped order selector

Abstract

Kernel density estimation (KDE) is a seasoned concept in nonparametric density estimation. KDE accuracy depends on the shape and the bandwidth of the kernel. However, the shape has only a minor influence on the estimation, whereas selecting proper bandwidth is critical. An alternative to kernel estimators are Bernstein density estimation (BDE) methods, which are gaining much interest recently. Like bandwidth selection in KDE, accurate order selection is critical in BDE. They are preferable over KDEs when the underling density is supported on an interval. They are naturally consistent at the boundaries and have low boundary bias. Like bandwidth selection in KDE, proper order selection is critical in BDE. Many authors have used cross-validation for data-driven order selection in the context of BDE. We will report on our findings from a simulation study that revealed some difficulties with cross-validation in this context. We will also mention the results of some of our investigations trying to address this issue and introduce bootstrapping as potential path for order selection in BDE.