Asymptotic Theory of Locally Conic Models and its Application to Multilayer Neural Networks
This paper discusses the maximum likelihood estimation in a statistical model with unidentiÞability, using the framework of conic singularity. The likelihood ratio may diverge in unidentiÞable cases, though in regular cases it converges to a χ distribution. A useful sufficient condition of such divergence is obtained, and is applied to neural networks. The exact order for multilayer perceptrons is also discussed.