Hierarchical mixtures-of-experts for exponential family regression models: Approximation and maximum likelihood estimation

• 成果类型: Article
• 署名作者: Jiang, WX; Tanner, MA
• 署名单位: Northwestern University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 987-1011
• 关键词: Bounds

摘要

We consider hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(alpha + x(T)beta) are mixed. Here psi(.) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form psi(h(x)) where h(.) is an element of W-2; K0(infinity) (a Sobolev class over [0, 1](s)). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m(-2/s)) in Hellinger distance and at a rate of O(m(-4/s)) in Kullback-Leibler divergence, where m is the number of experts, and s is the dimension of the predictor x. We also provide conditions under which the mean-square error of the estimated mean response obtained from the maximum likelihood method converges to zero, as the sample size and the number of experts both increase.