Abstract: We propose using the local kernel regression method to estimate the conditional mean function of a panel count model with time-varying coefficients. A partial log-likelihood with a local polynomial is used for the estimation. Under some regularity conditions, strong uniform consistency rates are obtained for the local estimator. For a fixed time point, we show that the local estimator converges in distribution to the normal distribution. Moreover, the Breslow-type estimation of the baseline mean function is shown to be consistent. Simulation studies show that the time-varying coefficient estimator is close to the true value, and that the empirical coverage probability of the confidence interval is close to the nominal level. Finally, we demonstrate the proposed method by applying it to analyze a clinical data set on childhood wheezing.

Key words and phrases: Cross-validation, kernel weight, local partial log-likelihood.