Nonparametric density estimation for spatial data with wavelets

JOURNAL OF MULTIVARIATE ANALYSIS

卷:166

Article

Krebs, Johannes T. N.¹ 

[1] Univ Calif Davis, Dept Stat, One Shields Ave, Davis, CA 95616 USA

关键词: Besov spaces;    Density estimation;    Hard thresholding;    Rate of convergence;    Spatial lattice processes;    Strong spatial mixing;    Wavelets;   

DOI  :  10.1016/j.jmva.2018.03.013

来源: Elsevier

【 摘 要 】

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 L-P' for p' is an element of[1,infinity). For this reason, we study density functions which are elements of a d-dimensional Besov space B-pq(s)(R-d). We also verify the analytic correctness of our results in numerical simulations. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free