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Neural Computation

July 1, 1996, Vol. 8, No. 5, Pages 1107-1122.
(doi: 10.1162/neco.1996.8.5.1107)
© 1996 Massachusetts Institute of Technology
Rate of Convergence in Density Estimation Using Neural Networks
Article PDF (637.22 KB)
Abstract

Given N i.i.d. observations {Xi}Ni=1 taking values in a compact subset of Rd, such that p* denotes their common probability density function, we estimate p* from an exponential family of densities based on single hidden layer sigmoidal networks using a certain minimum complexity density estimation scheme. Assuming that p* possesses a certain exponential representation, we establish a rate of convergence, independent of the dimension d, for the expected Hellinger distance between the proposed minimum complexity density estimator and the true underlying density p*.