Optimal Bandwidth Selection for Kernel Functional Estimation of Location and Scale Parameters

• Activity Number: 318
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Su Chen*
• Companies: University of Memphis
• Keywords: Optimal Bandwidth Selection ; Plug-in method ; MSE ; Kernel functional estimation

Abstract

The choice of bandwidth is crucial to the kernel density estimation (KDE) and kernel-based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. Ahmad (1982) proposed a new nonparametric estimate of location and scale parameters via the density functional estimation of a special case of the integration of \gamma(x)f^2(x). However, the optimal bandwidth selection for density functional estimation of location and scale parameters has not been examined. We propose a method to select the bandwidth for density functional estimation of the integration of \gamma(x)f^2(x). The idea underlying this method is to search for the optimal bandwidth for scale and location estimation by minimizing the mean square error (MSE) of their corresponding density functional estimate. Two practical bandwidth selection techniques for location and scale estimation are provided: normal scale bandwidth selection (namely "Rule of Thumb") and direct plug-in bandwidth selection.