Full bandwidth matrix selectors for gradient kernel density estimate

Authors:
Ivana Horová;Jan KoláčEk;Kamila Vopatová
Affiliations:
Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic;Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic;Department of Econometrics, University of Defence, Brno, Czech Republic
Venue:
Computational Statistics & Data Analysis
Year:
2013

Citing 4
Cited 2

A comparative study of several smoothing methods in density estimation

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Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernal density estimation

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Contribution to the bandwidth choice for kernel density estimates

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Feature significance for multivariate kernel density estimation

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Bayesian estimation of adaptive bandwidth matrices in multivariate kernel density estimation

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Abstract

The most important factor in multivariate kernel density estimation is a choice of a bandwidth matrix. This choice is particularly important, because of its role in controlling both the amount and the direction of multivariate smoothing. Considerable attention has been paid to constrained parameterization of the bandwidth matrix such as a diagonal matrix or a pre-transformation of the data. A general multivariate kernel density derivative estimator has been investigated. Data-driven selectors of full bandwidth matrices for a density and its gradient are considered. The proposed method is based on an optimally balanced relation between the integrated variance and the integrated squared bias. The analysis of statistical properties shows the rationale of the proposed method. In order to compare this method with cross-validation and plug-in methods the relative rate of convergence is determined. The utility of the method is illustrated through a simulation study and real data applications.