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Density estimation using Dirichlet kernels

Ouimet, Frédéric (2020) Density estimation using Dirichlet kernels. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200309-104903956

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Abstract

In this paper, we introduce Dirichlet kernels for the estimation of multivariate densities supported on the d-dimensional simplex. These kernels generalize the beta kernels from Brown & Chen (1999), Chen (1999), Chen (2000), Bouezmarni & Rolin (2003), originally studied in the context of smoothing for regression curves. We prove various asymptotic properties for the estimator: bias, variance, mean squared error, mean integrated squared error, asymptotic normality and uniform strong consistency. In particular, the asymptotic normality and uniform strong consistency results are completely new, even for the case d=1 (beta kernels). These new kernel smoothers can be used for density estimation of compositional data. The estimator is simple to use, free of boundary bias, allocates non-negative weights everywhere on the simplex, and achieves the optimal convergence rate of n−4/(d+4) for the mean integrated squared error.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2002.06956arXivDiscussion Paper
ORCID:
AuthorORCID
Ouimet, Frédéric0000-0001-7933-5265
Additional Information:F. O. is supported by a postdoctoral fellowship from the NSERC (PDF) and the FRQNT (B3X supplement). Preprint submitted to Elsevier.
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds de recherche du Québec – Nature et technologies (FRQNT)UNSPECIFIED
Record Number:CaltechAUTHORS:20200309-104903956
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200309-104903956
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101772
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:09 Mar 2020 17:56
Last Modified:09 Mar 2020 20:06

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