This paper studies the distribution estimation of contaminated data by the
MoM-GAN method, which combines generative adversarial net (GAN) and
median-of-mean (MoM) estimation. We use a deep neural network (DNN) with a ReLU
activation function to model the generator and discriminator of the GAN.
Theoretically, we derive a non-asymptotic error bound for the DNN-based MoM-GAN
estimator measured by integral probability metrics with the b-smoothness
H\"{o}lder class. The error bound decreases essentially as nβb/pβ¨nβ1/2, where n and p are the sample size and the dimension of input
data. We give an algorithm for the MoM-GAN method and implement it through two
real applications. The numerical results show that the MoM-GAN outperforms
other competitive methods when dealing with contaminated data