  For the conditional mean function of panel count model with time-varying
coefficients, we propose to use local kernel regression method for estimation.
Partial log-likelihood with local polynomial is formed for estimation. Under
some regularity conditions, strong uniform consistency rates are obtained for
the local estimator. At target time point, we show that the local estimator
converges in distribution to normal distribution. The baseline mean function
estimator is also shown to be consistent. Simulation studies show that the
time-varying coefficient estimator is close to the true value, the empirical
coverage probabilities of the confidence interval is close to the nominal
level. We also applied the proposed method to analyze a clinical study on
childhood wheezing.
