  We develop a pivotal test to assess the statistical significance of the
feature variables in a single-layer feedforward neural network regression
model. We propose a gradient-based test statistic and study its asymptotics
using nonparametric techniques. Under technical conditions, the limiting
distribution is given by a mixture of chi-square distributions. The tests
enable one to discern the impact of individual variables on the prediction of a
neural network. The test statistic can be used to rank variables according to
their influence. Simulation results illustrate the computational efficiency and
the performance of the test. An empirical application to house price valuation
highlights the behavior of the test using actual data.
