Mathematical Sciences: Generalized Linear Models

McCullagh教授将研究广义线性模型对多元离散响应的可能扩展。早期的结果表明，这类新模型是对数线性模型的一个有吸引力的替代方案。此外，McCullagh教授建议将早期关于线性模型中的色散效应的工作扩展到广义线性模型中的类似效应。将继续研究张量方法在理论统计和统计方法学问题中的应用。一个这样的问题是考虑定向累积量的傅立叶分解和衍生不变量作为工具在广义线性模型中基于残差估计累积量的问题。这项统计学研究是当前为广义线性模型提供理论的推动力的一部分。传统的线性模型假设响应变量是正态分布的。这项工作是将概念概率结构扩展到适用于多变量离散响应变量，并旨在基于这些模型开发适当的统计。

Professor McCullagh will investigate a possible extension of generalized linear models to multivariate discrete responses. Early results suggest that the new class of models is an attractive alternative to log-linear models. In addition, Professor McCullagh proposes to extend earlier work on dispersion effects in linear modles to analogous effects in generalized linear models. Investigation of the uses of tensor methods in problems of theoretical statistics and statistical methodology will be continued. One such problem is to consider the Fourier decomposition of directional cumulants and derived invariants as tools in the problem of estimating cumulants based on residuals in generalized linear models. This research in statistics is part of a current thrust to provide theory for generalized linear models. Traditional linear models assume the response variables are normally distributed. This work is to extend the conceptual probabilistic constructs to apply to multivariate discrete response variables, and aims at developing appropriate statistics based on these models.