Wavelet density estimation for negatively associated stratified size-biased sample

摘要

This paper provides upper bounds of wavelet estimations on L~p (l ≤ p ＜ ∞) risk for a density function in Besov spaces based on negatively associated stratified size-biased random samples. It turns out that the classical theorem of Donoho, Jphnstone, Kerkyacharian and Picard is completely extended to more general cases. More precisely, we consider the model with multiplication noise and allow the sample negatively associated. Our theory is illustrated with a simulation study.