  We consider the regression problem where the dependence of the response Y on
a set of predictors X is fully captured by the regression function E(Y |
X)=g(B'X), for an unknown function g and low rank parameter B matrix. We
combine neural networks with sufficient dimension reduction in order to remove
the limitation of small p and n of the latter. We show in simulations that the
proposed estimator is on par with competing sufficient dimension reduction
methods in small p and n settings, such as minimum average variance estimation
and conditional variance estimation. Among those, it is the only
computationally applicable in large p and n problems.
