Estimation and learning of network parameters in semiparametric stochastic perceptron

Kabashima and Shinomoto found (1992) that estimators of a binary decision boundary show asymptotically strange behaviors when the probability model is ill-posed or semiparametric. We give a rigorous analysis of this phenomenon in a stochastic perceptron by using the estimating function method. It is shown that there exists no estimator of threshold parameter h which converges to the true value in the order of 1/√n as the number n of observations increases. Instead we propose asymptotic estimating functions and analyze the asymptotics of the estimators therefrom