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AbstractWe develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the regression errors, showing that our method is most efficient when the correct covariance matrix is used. The component functions achieve the known asymptotic variance lower bound for the scalar argument case. Smooth backfitting also leads directly to design-independent biases in the local linear case. Simulations show our estimator has smaller variance than the usual kernel estimator. This is also illustrated by an example from nutritional epidemiology. © 2009 Biometrika Trust.
CitationCarroll RJ, Maity A, Mammen E, Yu K (2009) Nonparametric additive regression for repeatedly measured data. Biometrika 96: 383–398. Available: http://dx.doi.org/10.1093/biomet/asp015.
SponsorsThe authors are grateful to the editor, associate editor and two referees for their invaluable commentsand suggestions. Yu and Mammen’s research was supported by the Deutsche Forschungsgemeinschaft.Carroll and Maity’s research was supported by grants from the National CancerInstitute. Part of Carroll’s work was supported by an award made by the King Abdullah Universityof Science and Technology.
PublisherOxford University Press (OUP)