Restricted likelihood ratio lack-of-fit tests using mixed spline models

• 成果类型: Article
• 署名作者: Claeskens, G
• 署名单位: Universite Catholique Louvain; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2004.05421.x
• 发表日期: 2004
• 页码: 909-926
• 关键词: STATISTICAL-INFERENCE; linear-models; regression; asymptotics; selection

摘要

Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one-sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis. Conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies, and finite sample approximations to the asymptotic distribution are provided. Test statistics are studied for simple as well as multiple-regression models.