On the asymptotic normality of hierarchical mixtures-of-experts for generalized linear models

In the class of hierarchical mixtures-of-experts (HME) models, "experts" in the exponential family with generalized linear mean functions of the form /spl psi/(/spl alpha/+x/sup T//spl beta/) are mixed, according to a set of local weights called the "gating functions" depending on the predictor x. Here /spl psi/(/spl middot/) is the inverse link function. We provide regularity conditions on the experts and on the gating functions under which the maximum-likelihood method in the large sample limit produces a consistent and asymptotically normal estimator of the mean response. The regularity conditions are validated for Poisson, gamma, normal, and binomial experts.