Abstract: Panel count data are commonly encountered in analysis of recurrent events where the exact event times are unobserved. To accommodate the potential non-linear covariate effect, we consider a non-parametric regression model for panel count data. The regression B-splines method is used to estimate the regression function and the baseline mean function. The B-splines-based estimation is shown to be consistent and the rate of convergence is obtained. Moreover, the asymptotic normality for a class of smooth functionals of regression splines estimators is established. Numerical studies were carried out to evaluate the finite sample properties. Finally, we applied the proposed method to analyze the non-linear effect of one of interleukin functions with the risk of childhood wheezing.

Key words and phrases: Empirical process, maximum pseudolikelihood estimator, regression splines, wheezing.