Multivariate wavelet density estimation for strong mixing stratified size-biased sample

Abstract

This paper considers wavelet estimations of a multivariate density function based on stratified size-biased and strong mixing data. We provide upper bounds of the mean integrated squared error for linear and nonlinear wavelet estimators in Besov space It is shown that the linear estimator achieves the optimal convergence rate in the case of Moreover, the convergence rate of nonlinear estimator coincides with the optimal convergence rate up to a factor for In addition, the nonlinear wavelet estimator is adaptive.