A new asymptotic distribution for Hollanders bivariate symmetry statistic

Semiparametric statistical inference concepts are briefly reviewed and applied to artificial neural networks. We deal with asymptotic efficiency and robustness aspects of learning, two properties which represent key factors for the quality of the estimates that statisticians obtain. In particular, the accuracy of the estimates in the presence of outlying observations is an important goal since it is a well-known fact that between efficiency and robustness one seeks the best compromise. With that scope in mind, we analyze possible ways of building up net architectures without relying on strong assumptions about the functional components in the model.