Convergence Rates of Wavelet Density Estimators for Strongly Mixing Samples

This paper considers wavelet estimations for a multivariate density function based on strongly mixing data. We first construct a linear wavelet estimator and provide a convergence rate over Lp(1≤p ∞) risk in Besov space Bsr,q(Rd) . However, this estimator depends on the smoothness of density function, which means that the estimator is not adaptive. A nonlinear adaptive wavelet estimator is proposed by thresholding method. Moreover, the convergence rate of nonlinear estimator is better than the linear one in the case of r≤p .