Exploring the use of variable bandwidth kernel density estimators
Isaías H. Salgado-Ugarte
F.E.S. Zaragoza U.N.A.M. Biología &
Depto. de Biología, U.A.M. Iztapalapa
[email protected]
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Marco A. Pérez-Hernández
Depto. de Biología,
U.A.M. Iztapalapa; México
[email protected]
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Abstract. Variable bandwidth kernel density estimators increase the window width at
low densities and decrease it where data concentrate. This represents an
improvement over the fixed bandwidth kernel density estimators. In this
article, we explore the use of one implementation of a variable kernel
estimator in conjunction with several rules and procedures for bandwidth
selection applied to several real datasets. The considered examples permit
us to state that when working with tens or a few hundreds of data
observations, least-squares cross-validation bandwidth rarely produces
useful estimates; with thousands of observations, this problem can be
surpassed. Optimal bandwidth and biased cross-validation (BCV), in general,
oversmooth multimodal densities. The Sheather–Jones plug-in rule
produced bandwidths that behave slightly better in this respect. The
Silverman test is considered as a very sophisticated and safe procedure to
estimate the number of modes in univariate distributions; however, similar
results could be obtained with the Sheather–Jones rule, but at a much
lower computational cost. As expected, the variable bandwidth kernel density
estimates showed fewer modes than those chosen by the Silverman test,
especially those distributions in which multimodality was caused by several
noisy minor modes. More research on the subject is needed.
View all articles by these authors:
Isaías H. Salgado-Ugarte, Marco A. Pérez-Hernández
View all articles with these keywords:
kernel density estimation, bandwidth, cross validation, multimodality test
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