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Nonparametric density estimation for spatial data with wavelets

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  • Krebs, Johannes T.N.

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.

Suggested Citation

  • Krebs, Johannes T.N., 2018. "Nonparametric density estimation for spatial data with wavelets," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 300-319.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:300-319
    DOI: 10.1016/j.jmva.2018.03.013
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    References listed on IDEAS

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