Nonparametric adaptive density estimation on random fields using wavelet method

We consider non-linear wavelet-based estimators of density functions with stationary random fields, which are indexed by the integer lattice points in the N-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.