| Longitudinal data frequently appears in biomedical and epidemiological studies. Data sets usually involve repeatedly measured response variables and covariates on a set randomly chosen subjects over time, such as health status or disease progression. Longitudinal methods have been used to study the patterns of time-varying variables. One important goal of statistical analysis is to evaluate the effects of the covariates, which may or may not depend on time, on the response variable of interest. A well developed regression methodology could have important practical impacts in evaluating new medical treatment, identifying influential risk factors, verifying existing biological models, etc. The varying-coefficient model is a structural nonparametric model which is particularly useful in longitudinal analysis.; This dissertation studies a class of smoothing methods for estimation of the coefficient curves β(t) = (β0( t), β1(t),…,β k(t))T in the varying coefficient model Y(t) = X(t)β(t) + ϵ( t) for longitudinal data samples. A cross-validation criterion is adapted to select optimal smoothing parameters, and a bootstrap procedure is used to construct confidence intervals for the estimates. Asymptotic properties and inference are derived and a testing procedure is discussed for model diagnosis purpose. The proposed procedures are illustrated through data examples and demonstrated by simulation studies. |
