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Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines
Author(s) -
HUANG JIANHUA Z.,
ZHANG LIANGYUE,
ZHOU LAN
Publication year - 2007
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00550.x
Subject(s) - mathematics , semiparametric model , semiparametric regression , parametric statistics , marginal model , covariance , parametric model , estimating equations , spline (mechanical) , generalized estimating equation , moment (physics) , gaussian , statistics , econometrics , regression analysis , maximum likelihood , physics , structural engineering , classical mechanics , engineering , quantum mechanics
. We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non‐parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non‐parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption.