Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Abstract

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. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

Local asymptotic behavior of regression splines for marginal semiparametric models with longitudinal data

“…The variance is a dominating factor in comparison of the mean square error (MSE). The conclusions are consistent with [8]. In addition, the performance of the estimatorsβ based on the regression and smoothing splines are almost the same.…”

“…Let X and T denote, respectively, the collections of all X ij s and all T ij s. Similarly to [8], we give some expressions that are useful for further analysis. Let …”

“…To incorporate the correlation, Wang et al [6] and Chen and Jin [7] proposed many methods for semiparametric efficient estimation of partial linear model with longitudinal data by employing the iterative kernel method and the piecewise polynomials method respectively. Huang et al [8] considered efficient estimation in marginal partially linear model for longitudinal data through splines. However, an explicit expression for the asymptotic bias of the estimate of the nonparametric function f (·) was not given.…”

Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function

“…It is a natural extension of the models studied by Lin and Carroll (2001) (with identity link), He, Zhu, and Fung (2002), He, Fung, and Zhu (2005), Wang, Carroll, and Lin (2005), and Huang and Zhang (2004). We focus on parsimonious modeling of the covariance function of the random error process ε(t) for the analysis of longitudinal data, when observations are collected at irregular and possibly subject-specific time points.…”

Smooth-threshold GEE variable selection for varying coefficient partially linear models with longitudinal data

“…The proof of (A.17) relies heavily on the empirical process theory and is similar to Huang, Zhang, and Zhou (2007) and we omit the details. According to (A.16) and (A.17), we complete the whole proof of Theorem 3.…”