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Nonparametric additive regression for repeatedly measured data

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  • Raymond J. Carroll
  • Arnab Maity
  • Enno Mammen
  • Kyusang Yu

Abstract

We 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. Copyright 2009, Oxford University Press.

Suggested Citation

  • Raymond J. Carroll & Arnab Maity & Enno Mammen & Kyusang Yu, 2009. "Nonparametric additive regression for repeatedly measured data," Biometrika, Biometrika Trust, vol. 96(2), pages 383-398.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:383-398
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    File URL: http://hdl.handle.net/10.1093/biomet/asp015
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    Cited by:

    1. Enno Mammen & Byeong U. Park & Melanie Schienle, 2012. "Additive Models: Extensions and Related Models," SFB 649 Discussion Papers SFB649DP2012-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Shujie Ma & Jeffrey S. Racine, 2012. "Additive Regression Splines With Irrelevant Categorical and Continuous Regressors," Department of Economics Working Papers 2012-07, McMaster University.
    3. Ma, Haiqiang & Zhu, Zhongyi, 2016. "Continuously dynamic additive models for functional data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 1-13.
    4. Al Kadiri, M. & Carroll, R.J. & Wand, M.P., 2010. "Marginal longitudinal semiparametric regression via penalized splines," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1242-1252, August.

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