Abstract
We consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carroll RJ, Maity A, Mammen E, Yu K (2009) Nonparametric additive regression for repeatedly measured data. Biometrika, to appear
Chatterjee N, Kalaylioglu Z, Moslehi R, Peters U, Wacholder S (2006) Powerful multi-locus tests for genetic association in the presence of gene–gene and gene–environment interactions. Am J Human Genet 79:1002–1016
Fan J, Gijbels I (1996) Local polynomial modeling and its applications. Chapman and Hall, London
Härdle W, Liang H, Gao J (2000) Partially linear models. Physica Verlag, Heidelberg
Kipnis V, Subar AF, Midthune D, Freedman LS, Ballard-Barbash R, Troiano R, Bingham S, Schoeller DA, Schatzkin A, Carroll RJ (2003) The structure of dietary measurement error: results of the OPEN biomarker study. Am J Epidemiol 158:14–21
Lin X, Carroll RJ (2006) Semiparametric estimation in general repeated measures problems. J R Stat Soc Ser B 68:68–88
Lu Z, Lundervold L, Tjøstheim D, Yao Q (2007) Exploring spatial nonlinearity using additive approximation. Bernoulli 13:447–472
Maity A, Ma Y, Carroll RJ (2007) Efficient estimation of population-level summaries in general semiparametric regression models with missing response. J Am Stat Assoc 102:123–139
Maity A, Carroll RJ, Mammen E, Chatterjee N (2009) Powerful multi-locus tests for genetic association with semiparametric gene–environment interactions. J R Stat Soc Ser B 71:75–96
van de Geer S (2000) Empirical processes in M-estimation. Cambridge University Press, Cambridge
Wang N (2003) Marginal nonparametric kernel regression accounting for within-subject correlation. Biometrika 90:43–52
Wang N, Carroll RJ, Lin X (2005) Efficient semiparametric marginal estimation for longitudinal/clustered data. J Am Stat Assoc 100:147–157
Willett WC (1990) Nutritional epidemiology. Oxford University Press, New York
Yu K, Mammen E, Park B (2009) Semiparametric additive regression: gains from the additive structure of the infinite dimensional parameter. Preprint
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carroll, R., Maity, A., Mammen, E. et al. Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data. Stat Biosci 1, 10–31 (2009). https://doi.org/10.1007/s12561-009-9000-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12561-009-9000-7