Multivariate wavelet-based density estimation with size-biased data

In this paper, we employ wavelet method to propose a multivariate density estimator based on a biased sample. We investigate the asymptotic rate of convergence of the proposed estimator over a large class of densities in the Besov space, Bpqs. Moreover, we prove the consistency of our estimator when the expectation of weight function is unknown. This paper is an extension of results in Ramirez and Vidakovic (2010) and Chesneau et al. (2012) to the multivariate case.