Local Estimation of a Multivariate Density and its Derivatives

We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of weighted scoring rules with local quadratic models. The...

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Bibliographic Details
Published in:arXiv.org 2020-08
Main Authors: Strähl, Christof, Ziegel, Johanna F, Duembgen, Lutz
Format: Article
Language:English
Subjects:
Density
Derivatives
Polynomials
Online Access:Get full text
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Summary:We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of weighted scoring rules with local quadratic models. The other two approaches are matching of local moments and kernel density estimation. All estimators depend on a general kernel, and we use the Gaussian kernel to provide explicit examples. Asymptotic properties of the estimators are derived and compared. In terms of rates of convergence, a refined local moment matching estimator is the best.
ISSN:2331-8422