Nonparametric Estimation of Multiplicative Counting Process Intensity Functions with an Application to the Beijing SARS Epidemic

The local polynomial methods and martingale estimating equations are used to develop closed form estimators of the intensity function and its derivatives for multiplicative counting process models. The consistency and asymptotic normality of the estimators are established. The estimator generalizes that proposed by Ramlau-Hansen (1983 Ramlau-Hansen , H. ( 1983 ). Smoothing counting process intensities by means of kernel function . Ann. Statist. 11 ( 2 ): 453 – 466 .[Crossref] , [Google Scholar]) with a smaller bias than the Ramlau-Hansen intensity estimator. The derivative estimators give smoother estimates than the Ramlau-Hansen derivative estimators. The proposed estimators are applied to analyze the infection rate and its derivatives of the 2003 Severe Acute Respiratory Syndrome (SARS) epidemic in Beijing, China.