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Nonparametric Varying‐Coefficient Models for the Analysis of Longitudinal Data
Author(s) -
Wu Colin O.,
Yu Kai F.
Publication year - 2002
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2002.tb00176.x
Subject(s) - nonparametric statistics , covariate , econometrics , computer science , curse of dimensionality , parametric statistics , statistical inference , semiparametric regression , statistics , data set , inference , parametric model , mathematics , machine learning , artificial intelligence
Summary Longitudinal methods have been widely used in biomedicine and epidemiology to study the patterns of time‐varying variables, such as disease progression or trends of health status. Data sets of longitudinal studies usually involve repeatedly measured outcomes and covariates on a set of randomly chosen subjects over time. An important goal of statistical analyses is to evaluate the effects of the covariates, which may or may not depend on time, on the outcomes of interest. Because fully parametric models may be subject to model misspecification and completely unstructured nonparametric models may suffer from the drawbacks of “curse of dimensionality”, the varying‐coefficient models are a class of structural nonparametric models which are particularly useful in longitudinal analyses. In this article, we present several important nonparametric estimation and inference methods for this class of models, demonstrate the advantages, limitations and practical implementations of these methods in different longitudinal settings, and discuss some potential directions of further research in this area. Applications of these methods are illustrated through two epidemiological examples.