@article{Kou2024, 
author = {Junke Kou and Xianmei Chen},
title = {Wavelet estimations of a density function in two-class mixture model},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {20588-20611},
keywords = {nonparametric estimation, wavelet estimator, density function, convergence rate},
url = {https://www.sciopen.com/article/10.3934/math.20241000},
doi = {10.3934/math.20241000},
abstract = {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  Lp(1≤p<+∞) risk of those wavelet estimators are proved in Besov spaces. When  p~≥p≥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≤p~<p. Finally, some numerical experiments are presented to validate the theoretical results.}
}