Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data

• 成果类型: Article
• 署名作者: Hu, ZH; Wang, NY; Carroll, RJ
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/91.2.251
• 发表日期: 2004
• 页码: 251262
• 关键词: regression

摘要

We study the profile-kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root-n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profile-kernel method; that is, for clustered data, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profile-kernel estimator. Consequently, the common practice of using the backfitting method to compute profile-kernel estimates is no longer advised. We illustrate this in detail by following Zeger & Diggle (1994) and Lin & Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described.