Many systems experience recurrent events. Recurrence data are collected to analyze quantities of interest, such as the mean cumulative number of events. Methods of analysis are available for recurrence data with left and/or right censoring. Due to practical constraints, however, recurrence data are sometimes recorded only in windows. Between the windows are gaps over which the process cannot be observed. This article extends existing statistical methods, both nonparametric and parametric, to window-observation recurrence data. The nonparametric estimator requires minimum assumptions but will be inconsistent if the size of the risk set is not positive over the entire period of interest. No such difficulty arises when using a parametric model for the recurrence data. For cases in which the size of the risk set is zero for some period of time, we propose and compare two alternative hybrid estimators. We illustrate the methods with two example applications.
['Jianying Zuo', 'William Q. Meeker', 'Huaiqing Wu']
Analysis of Window-Observation Recurrence Data