Nonparametric density estimation for spatial data with wavelets

Johannes T.N. Krebs

Journal of Multivariate Analysis, 2018, vol. 166, issue C, 300-319

Abstract: Nonparametric density estimators are studied for d-dimensional, strongly spatial mixing data which are defined on a general N-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators derived from a d-dimensional multi-resolution analysis. We give sufficient criteria for the consistency of these estimators and derive rates of convergence in Lp′ for p′∈[1,∞). For this reason, we study density functions which are elements of a d-dimensional Besov space Bp,qs(Rd). We also verify the analytic correctness of our results in numerical simulations.

Keywords: Besov spaces; Density estimation; Hard thresholding; Rate of convergence; Spatial lattice processes; Strong spatial mixing; Wavelets (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:166:y:2018:i:c:p:300-319

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DOI: 10.1016/j.jmva.2018.03.013

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