A flexible approach to inference in semiparametric regression models with correlated errors using Gaussian processes

详细信息    查看全文

• 作者：Heping He^a ; ^{heping.he@outlook.com" class="auth_mail" title="E-mail the corresponding author} ; Thomas A. Severini^b ; ^{severini@northwestern.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semiparametric model ; Gaussian process regression ; Generalized least squares ; Restricted maximum likelihood
• 刊名：Computational Statistics & Data Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：103
• 期：Complete
• 页码：316-329
• 全文大小：599 K

文摘

Consider a semiparametric regression model in which the mean function depends on a finite-dimensional regression parameter as the parameter of interest and an unknown function as a nuisance parameter. A method of inference in such models is proposed, using a type of integrated likelihood in which the unknown function is eliminated by averaging with respect to a given distribution, which we take to be a Gaussian process with a covariance function chosen to reflect the assumptions about the function. This approach is easily implemented and can be applied to a wide range of models using the same basic methodology. The consistency and asymptotic normality of the estimator of the parameter of interest are established under mild conditions. The proposed method is illustrated on several examples.