On the Asymptotic Normality of Hierarchical Mixtures-of-Experts for Generalized Linear Models (1999)
| Venue: | IEEE Trans. on Information Theory |
| Citations: | 4 - 0 self |
BibTeX
@ARTICLE{Jiang99onthe,
author = {Wenxin Jiang and Martin A. Tanner},
title = {On the Asymptotic Normality of Hierarchical Mixtures-of-Experts for Generalized Linear Models},
journal = {IEEE Trans. on Information Theory},
year = {1999},
volume = {46},
pages = {1005--1013}
}
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Abstract
In the class of hierarchical mixtures-of-experts (HME) models, "experts" in the exponential family with generalized linear mean functions of the form /(ff + x T fi) are mixed, according to a set of local weights called the "gating functions" depending on the predictor x. Here /(\Delta) 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. Index Terms --- Hierarchical mixtures-of-experts, generalized linear models, maximum likelihood estimation, large sample theory, asymptotic normal distribution, regularity conditions, Fisher information, statistical inference. 1 Introduction In Hierarchical Mixtures-of-Experts (HME) (Jordan and Jacobs 1994), experts of simple regression models are mixed in a tree-s...
