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Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation. (English) Zbl 1066.62059
Summary: Progress in selection of smoothing parameters for kernel density estimation has been much slower in the multivariate than univariate setting. Within the context of multivariate density estimation attention has focused on diagonal bandwidth matrices. However, there is evidence to suggest that the use of full (or unconstrained) bandwidth matrices can be beneficial. This paper presents some results in the asymptotic analysis of data-driven selectors of full bandwidth matrices. In particular, we give relative rates of convergence for plug-in selectors and a biased cross-validation selector.

MSC:
62H12 Estimation in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
Software:
KernSmooth; pyuvdata
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References:
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