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A combined adaptive-mixtures/plug-in estimator of multivariate probability densities. (English) Zbl 0915.62021
Summary: A multivariate extension of the plug-in kernel (and filtered kernel) estimator is proposed and uses the asymptotically optimal bandwidth matrix (matrices) for a normal mixture approximation of a density to be estimated (the filtered kernel estimator uses different matrices for different clusters of data). The normal mixture approximation is provided by a recursive version of the EM algorithm whose initial conditions are in turn obtained via an application of the ideas of adaptive mixtures density estimation and AIC-based pruning. Simulations show that the estimator proposed, while it is in fact a rather complex multistage estimation process, provides a very reliable way of estimating arbitrary and highly structured continuous densities in \({\mathbb{R}}^{2}\) and, hopefully, \({\mathbb{R}}^{3}\).

MSC:
62G07 Density estimation
62H12 Estimation in multivariate analysis
Software:
KernSmooth
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