Article ID Journal Published Year Pages File Type
1151599 Statistics & Probability Letters 2015 10 Pages PDF
Abstract

We consider non-linear wavelet-based estimators of density functions with stationary random fields, which are indexed by the integer lattice points in the NN-dimensional Euclidean space and are assumed to satisfy some mixing conditions. We investigate their asymptotic rates of convergence based on thresholding of empirical wavelet coefficients and show that these estimators achieve nearly optimal convergence rates within a logarithmic term over a large range of Besov function classes Bp,qs. Therefore, wavelet estimators still achieve nearly optimal convergence rates for random fields and provide explicitly the extraordinary local adaptability.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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