Semiparametric and Nonparametric Regression Analysis of Longitudinal Data

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Abstract
This article deals with the regression analysis of repeated measurements taken at irregular and possibly subject-specific time points. The proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable Y at time t is related to the vector of possibly time-varying covariates X through the equations E{Y(t)|| X(t} = α0(t) + β′0X(t) and E{Y(t)||X(t)} = α0(t)+ β′0(t)X(t), where α0(t) is an arbitrary function of t, β0 is a vector of constant regression coefficients, and β0(t) is a vector of time-varying regression coefficients. The stochastic structure of the process Y(·) is completely unspecified. We develop a class of least squares type estimators for β0, which is proven to be n½-consistent and asymptotically normal with simple variance estimators. Furthermore, we develop a closed-form estimator for a cumulative function of β0(t), which is shown to be n½-consistent and, on proper normalization, converges weakly to a zero-mean Gaussian pr...