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Abstract:
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In longitudinal/clustered data analysis, the popular marginal partial linear models are Y_{ij}=f(t_{ij})+ X_{ij} \beta + \epsilon_{ij}, where Y_{ij} is the j-th measurement taken on the i-th subject at time t_{ij}, f is an unknown smooth function, X_{ij}'s are covariate variables, and \epsilon_{ij}'s are random mean 0 errors with possible within-subject correlation. Assuming that the correlation structure of the random errors depends on a few parameters, we consider two estimation procedures using smoothing splines and propose a method to jointly select the smoothing parameter and the correlation parameters. The asymptotic optimality of the estimates was established together with the \sqrt{n} convergence rates of the correlation parameters and the \sqrt{n} normality of the \beta estimates. Application to the CD4 data is also presented.
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