Cross Validation Bandwidth Selection for Derivatives of Multidimensional Densities

by Matthew D. Baird

Download Free Electronic Document

FormatFile SizeNotes
PDF file 0.2 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.

Little attention has been given to the effect of higher order kernels for bandwidth selection for multidimensional derivatives of densities. This paper investigates the extension of cross validation methods to higher dimensions for the derivative of an unconditional joint density. I present and derive different cross validation criteria for arbitrary kernel order and density dimension, and show consistency of the estimator. Doing a Monte Carlo simulation study for various orders of kernels in the Gaussian family and additionally comparing a weighted integrated square error criterion, I find that higher order kernels become increasingly important as the dimension of the distribution increases. I find that standard cross validation selectors generally outperform the weighted integrated square error cross validation criteria. Using the infinite order Dirichlet kernel tends to have the best results.

This paper series made possible by the RAND Center for the Study of Aging and the RAND Population Research Center.

This report is part of the RAND Corporation Working paper series. RAND working papers are intended to share researchers' latest findings and to solicit informal peer review. They have been approved for circulation by RAND but may not have been formally edited or peer reviewed.

Permission is given to duplicate this electronic document for personal use only, as long as it is unaltered and complete. Copies may not be duplicated for commercial purposes. Unauthorized posting of RAND PDFs to a non-RAND Web site is prohibited. RAND PDFs are protected under copyright law. For information on reprint and linking permissions, please visit the RAND Permissions page.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.