Spades and mixture models
F. Bunea, A.B. Tsybakov and M.H. Wegkamp
Annals of Statistics
This paper studies sparse density estimation via L1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax
adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy.