On the asymptotics of marginal regression splines with longitudinal data

• 成果类型: Article
• 署名作者: Zhu, Zhongyi; Fung, Wing K.; He, Xuming
• 署名单位: Fudan University; University of Hong Kong; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn041
• 发表日期: 2008
• 页码: 907917
• 关键词: Nonparametric regression; local asymptotics; linear-models

摘要

There have been studies on how the asymptotic efficiency of a nonparametric function estimator depends on the handling of the within-cluster correlation when nonparametric regression models are used on longitudinal or cluster data. In particular, methods based on smoothing splines and local polynomial kernels exhibit different behaviour. We show that the generalized estimation equations based on weighted least squares regression splines for the nonparametric function have an interesting property: the asymptotic bias of the estimator does not depend on the working correlation matrix, but the asymptotic variance, and therefore the mean squared error, is minimized when the true correlation structure is specified. This property of the asymptotic bias distinguishes regression splines from smoothing splines.