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Cross‐validation Bandwidth Matrices for Multivariate Kernel Density Estimation
Author(s) -
DUONG TARN,
HAZELTON MARTIN L.
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00445.x
Subject(s) - bandwidth (computing) , kernel density estimation , univariate , mathematics , multivariate statistics , diagonal , cross validation , diagonal matrix , statistics , multivariate analysis , algorithm , computer science , telecommunications , estimator , geometry
. The performance of multivariate kernel density estimates depends crucially on the choice of bandwidth matrix, but progress towards developing good bandwidth matrix selectors has been relatively slow. In particular, previous studies of cross‐validation (CV) methods have been restricted to biased and unbiased CV selection of diagonal bandwidth matrices. However, for certain types of target density the use of full (i.e. unconstrained) bandwidth matrices offers the potential for significantly improved density estimation. In this paper, we generalize earlier work from diagonal to full bandwidth matrices, and develop a smooth cross‐validation (SCV) methodology for multivariate data. We consider optimization of the SCV technique with respect to a pilot bandwidth matrix. All the CV methods are studied using asymptotic analysis, simulation experiments and real data analysis. The results suggest that SCV for full bandwidth matrices is the most reliable of the CV methods. We also observe that experience from the univariate setting can sometimes be a misleading guide for understanding bandwidth selection in the multivariate case.