Abstract
We study partially linear models for asynchronous longitudinal data to incorporate nonlinear time trend effects. Local and global estimating equations are developed for estimating the parametric and nonparametric effects. We show that with a proper choice of the kernel bandwidth parameter, one can obtain consistent and asymptotically normal parameter estimates for the linear effects. Asymptotic properties of the estimated nonlinear effects are established. Extensive simulation studies provide numerical support for the theoretical findings. Data from an HIV study are used to illustrate our methodology.
Highlights
Asynchronous longitudinal data refers to the data structure that measurement times for the longitudinal response and longitudinal covariates are mismatched within individuals
We study the partially linear models for asynchronous longitudinal data: E{Y (t)|X(t)} = α(t) + X(t)T β, (1.1)
We propose a semiparametric partially linear model for asynchronous longitudinal data analysis
Summary
Asynchronous longitudinal data refers to the data structure that measurement times for the longitudinal response and longitudinal covariates are mismatched within individuals. Cao et al (2015) proposed a nonparametric kernel weighting approach for the generalized linear models to explicitly deal with the asynchronous structure and rigorously established the consistency and asymptotic normality of the resulting estimates. This was extended to a more general set up in Cao et al (2016). Unlike Lin and Ying (2001); Fan and Li (2004) for synchronous longitudinal data, a global estimating equation is proposed to down-weigh those observations which are distant in time and enables the use of all covariate observations for each observed response with asynchronous longitudinal data.
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