Kernel smoothing on varying coefficient models with longitudinal dependentvariable

This paper considers a nonparametric varying coefficient regression model w ith longitudinal dependent variable and cross-sectional covariates. The rel ationship between the dependent variable and the covariates is assumed to b e linear at a specific time point, but the coefficients are allowed to chan ge over time. Two kernel estimators based on componentwise local least squa res criteria are proposed to estimate the time varying coefficients. A cros s-validation criterion and a bootstrap procedure are used for selecting dat a-driven bandwidths and constructing confidence intervals, respectively. Th e theoretical properties of our estimators are developed through their asym ptotic mean squared errors and mean integrated squared errors. The finite s ample properties of our procedures are investigated through a simulation st udy. Applications of our procedures are illustrated through an epidemiologi cal example of predicting the effects of cigarette smoking, pre-HIV infecti on CD4 cell percentage and age at HIV infection on the depletion of CD4 cel l percentage among HIV infected persons.