Cover: Cross Validation Bandwidth Selection for Derivatives of Multidimensional Densities

Cross Validation Bandwidth Selection for Derivatives of Multidimensional Densities

Published Dec 5, 2014

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 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.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND 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.