KERNEL SMOOTHING ON VARYING COEFFICIENT MODELS WITH LONGITUDINAL DEPENDENT VARIABLE

Abstract

This paper considers a nonparametric varying coefficient regression model with longitudinal dependent variable and cross-sectional covariates. The relation- ship between the dependent variable and the covariates is assumed to be linear at a specific time point, but the coefficients are allowed to change over time. Two kernel estimators based on componentwise local least squares criteria are proposed to esti- mate the time varying coefficients. A cross-validation criterion and a bootstrap pro- cedure are used for selecting data-driven bandwidths and constructing confidence intervals, respectively. The theoretical properties of our estimators are developed through their asymptotic mean squared errors and mean integrated squared errors. The finite sample properties of our procedures are investigated through a simulation study. Applications of our procedures are illustrated through an epidemiological example of predicting the effects of cigarette smoking, pre-HIV infection CD4 cell percentage and age at HIV infection on the depletion of CD4 cell percentage among HIV infected persons.