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Mathematics > Statistics Theory

arXiv:1812.09322 (math)
[Submitted on 21 Dec 2018 (v1), last revised 10 Aug 2020 (this version, v2)]

Title:Local Estimation of a Multivariate Density and its Derivatives

Authors:Christof Strähl, Johanna F. Ziegel, Lutz Duembgen
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Abstract: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 Hyvärinen 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.
Comments: 41 pages
Subjects: Statistics Theory (math.ST)
MSC classes: 62G07, 62F12
Cite as: arXiv:1812.09322 [math.ST]
  (or arXiv:1812.09322v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.1812.09322

Submission history

From: Christof Strähl [view email]
[v1] Fri, 21 Dec 2018 16:15:44 UTC (44 KB)
[v2] Mon, 10 Aug 2020 15:18:30 UTC (38 KB)
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