A Brief Survey of Bandwidth Selection for Density Estimation

Jones, M. C.; Marron, J. S.; Sheather, Simon J.

doi:10.2307/2291420

Cited by 566 publications

(601 citation statements)

References 27 publications

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“…It can be easily extended to a multivariate setting. Several sophisticated methods to select the smoothing parameter included in the estimator have been developed, so that the technique is now fully data-based (Jones et al 1996;Duong and Hazelton 2003, 2005a, 2005b. We show here that f can be seen as a variant of the kernel density estimator.…”

Section: Related Methodsmentioning

confidence: 95%

Density estimation with minimization of U-divergence

Naito

Eguchi

2012

Mach Learn

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This paper is concerned with density estimation based on the stagewise minimization of the U -divergence. The U -divergence is a general divergence measure involving a convex function U which includes the Kullback-Leibler divergence and the L 2 norm as special cases. The algorithm to yield the density estimator is closely related to the boosting algorithm and it is shown that the usual kernel density estimator can also be seen as a special case of the proposed estimator. Non-asymptotic error bounds of the proposed estimators are developed and numerical experiments show that the proposed estimators often perform better than several existing methods for density estimation.

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Section: Related Methodsmentioning

confidence: 95%

Density estimation with minimization of U-divergence

Naito

Eguchi

2012

Mach Learn

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“…By default, the abanico plot uses the method of Sheather and Jones (1991) to derive a suitable bandwidth (cf. Jones et al 1996 for a methodological comparison). KDE plots are the default option for the univariate part of the abanico plot, mainly because they provide a reasonable picture of the underlying distribution of z i for a sufficiently large number of samples.…”

Section: Philosophy and Constructionmentioning

confidence: 99%

The abanico plot: Visualising chronometric data with individual standard errors

Dietze

Kreutzer

Burow

et al. 2016

Quaternary Geochronology

109

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Numerical dating methods in Quaternary science are faced with the need to adequately visualise data consisting of estimates that have differing standard errors. Recent approaches either focus on the display of age frequency distributions that ignore the standard errors or on radial plots, that allow comparisons between estimates allowing for their differing precisions, but without giving an explicit picture of the age frequency distribution. Hence, visualising both aspects requires at least two plots. Here, an alternative is introduced: The abanico plot. It combines both aspects and therefore allows comprehensive presentation of chronometric data with individual standard errors. It extends the radial plot by a kernel density estimate plot, histogram or dot plot and contains elements that link both plot types. As part of the R package 'Luminescence' (version 0.4.5), the abanico plot is designed as the final part of a comprehensive analysis chain of luminescence data but is open to a wide range of other Quaternary dating communities, as illustrated by several examples.

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“…Obtaining similar highly stable data-based nearly optimal bandwidth estimators requires very sophisticated estimates of the roughness function given in Equation 1. One algorithm by Hall et al (1991) is often highly rated in practice (Jones et al, 1996). Scott (1992) noted the small-sample behavior of the algorithm seemed closely related to the oversmoothed bandwidths.…”

Section: Oversmoothed Bandwidthsmentioning

confidence: 99%

Multivariate Density Estimation and Visualization

Scott

2011

Handbook of Computational Statistics

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A Brief Survey of Bandwidth Selection for Density Estimation

Cited by 566 publications

References 27 publications

Density estimation with minimization of U-divergence

Density estimation with minimization of U-divergence

The abanico plot: Visualising chronometric data with individual standard errors

Multivariate Density Estimation and Visualization

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