RATE OF CONVERGENCE IN DENSITY-ESTIMATION USING NEURAL NETWORKS

Given Ni.i.d. observations {X(i)}(N)(i=1) taking values in a compact s ubset of R(d), such that p denotes their common probability density f unction, we estimate p from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum comp lexity density estimation scheme. Assuming that p possesses a certain exponential representation, we establish a rate of convergence, indep endent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underl ying density p.