Choosing a Kernel for Cross-Validation

• Main Author: Savchuk, Olga
• Other Authors: Hart, Jeffrey D.
• Format: Others
• Language: en_US
• Published: 2010
• Subjects: bandwidth selection; cross-validation; kernel density estimation; kernel regression; nonparametric function estimation
• Online Access: http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-7002; http://hdl.handle.net/1969.1/ETD-TAMU-2009-08-7002

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.