Wavelet estimations of a density function in two-class mixture model

This paper considers nonparametric estimations of a density function in a two-class mixture model. A linear wavelet estimator and an adaptive wavelet estimator are constructed. Upper bound estimations over $L^p(1\le p<+\mathrm{\infty })$ risk of those wavelet estimators are proved in Besov spaces. When $\tilde{p}\ge p\ge 1$, the convergence rate of adaptive wavelet estimator is the same as the linear estimator up to a $\ln n$ factor. The adaptive wavelet estimator can get better than the linear estimator in the case of $1\le \tilde{p}<p$. Finally, some numerical experiments are presented to validate the theoretical results.