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Partial Linear Models for Longitudinal Data Based on Quadratic Inference Functions
Author(s) -
BAI YANG,
ZHU ZHONGYI,
FUNG WING K.
Publication year - 2008
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.1467-9469.2007.00578.x
Subject(s) - mathematics , inference , semiparametric model , parametric statistics , estimating equations , semiparametric regression , quadratic equation , spline (mechanical) , statistical inference , parametric model , statistics , computer science , maximum likelihood , artificial intelligence , geometry , structural engineering , engineering
. In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non‐parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.