Speaker: Zhao Ren

Abstract: This will be a combination of a paper by Liu and Gao on robust density estimation under pointwise L_2 loss (at a fixed point), along with some ongoing work on density estimation under L_p loss. Please see the paper for abstract of the first work (easier to parse the mathematical expressions in pdf). A rough summary of the of the second work is as follows. We revisit the classical non-parametric density estimation under Huber's contamination model and consider various L_p losses. We carefully study the effect of contamination on the rate-optimal estimation over a scale of the anisotropic Nikolskii classes. We also develop new adaptive procedures and derive the corresponding L_p risk oracle inequalities. Our technical analysis in adaptive procedures relies on some uniform bounds under the L_p norm of empirical processes developed by Goldenshluger and Lepski.