New Kernel Density Estimates and Their Empirical Likelihood Versions and Applications

• Activity Number: 305
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): ningning wang*+ and Ibrahim Ahmad
• Companies: and Oklahoma state university
• Keywords: kernel ; empirical likelihood ; AMISE ; bandwidth ; humps

Abstract

Kernel density estimation has been for several decades one of the most active areas of research in Nonparametric Statistics. Some flaws in the methodology include Bandwidth selection techniques that may or may not work. Catching the humps is difficult. Adopting the estimate to sequential sampling is difficult. Curse of dimensionality makes this methodology difficult to use in multidimensional settings.

This work presents a new class of two different kernel estimates and discusses them. The new estimates solve several of the above problems. The bandwidth selection is much tighter and hence it more accurately catches distribution humps and valleys. The estimates can be used both for fixed and sequential sampling.

Empirical likelihood (EL) versions of the estimates are given and shown to have AMISE smaller than that of the non-EL estimates, where the difference tends to shrink as the sample size rises.

Applications of the new estimates are discussed leading to new estimates and their EL versions for the cumulative distribution function, regression, and estimation of the location and scale parameters. Bandwidth selection problems in the above applications are also derived.