In this thesis, we apply neural network method to estimate nonparametric conditional quantile under the quantile regression loss, i.e., the check loss function. The proposed robust neural network (RNN) method integrates quantile regression
and neural network together, and is a useful modelling tool. We further apply an
majorization-minization (MM) algorithm (Hunter & Lange, 2000) to deal with the minimization of RNN. Monte Carlo simulation study is conducted to examine the performance of the proposed robust neural network. From our simulation results,
we found that the RNN method is promising. The proposed procedures are illustrated and compared with two popular nonparametric methods, local linear and regression splines, by a real data example in credit card portfolio analysis.
