A Caltech Library Service

Density estimation using Dirichlet kernels

Ouimet, Frédéric (2020) Density estimation using Dirichlet kernels. . (Unpublished)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 Paper
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.
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:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101772
Deposited By: Joy Painter
Deposited On:09 Mar 2020 17:56
Last Modified:09 Mar 2020 20:06

Repository Staff Only: item control page