Choosing a Kernel for Cross-Validation
Abstract
The statistical properties of cross-validation bandwidths can be improved by choosing
an appropriate kernel, which is different from the kernels traditionally used for cross-
validation purposes. In the light of this idea, we developed two new methods of
bandwidth selection termed: Indirect cross-validation and Robust one-sided cross-
validation. The kernels used in the Indirect cross-validation method yield an
improvement in the relative bandwidth rate to n^1=4, which is substantially better
than the n^1=10 rate of the least squares cross-validation method. The robust kernels
used in the Robust one-sided cross-validation method eliminate the bandwidth bias
for the case of regression functions with discontinuous derivatives.
Subject
bandwidth selectioncross-validation
kernel density estimation
kernel regression
nonparametric function estimation
Citation
Savchuk, Olga (2009). Choosing a Kernel for Cross-Validation. Doctoral dissertation, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /ETD -TAMU -2009 -08 -7002.