Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data

• 成果类型: Article
• 署名作者: Wang, Bo; Shi, Jian Qing
• 署名单位: University of Leicester; Newcastle University - UK
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.889021
• 发表日期: 2014
• 页码: 1123-1133
• 关键词: varying coefficient models; bayesian-inference; Consistency

摘要

In this article, we propose a generalized Gaussian process concurrent regression model for functional data, where the functional response variable has a binomial, Poisson, or other non-Gaussian distribution from an exponential family, while the covariates are mixed functional and scalar variables. The proposed model offers a nonparametric generalized concurrent regression method for functional data with multidimensional covariates, and provides a natural framework on modeling common mean structure and covariance structure simultaneously for repeatedly observed functional data. The mean structure provides overall information about the observations, while the covariance structure can be used to catch up the characteristic of each individual batch. The prior specification of covariance kernel enables us to accommodate a wide class of nonlinear models. The definition of the model, the inference, and the implementation as well as its asymptotic properties are discussed. Several numerical examples with different non-Gaussian response variables are presented. Some technical details and more numerical examples as well as an extension of the model are provided as supplementary materials.