Optimal goodness-of-fit tests for recurrent event data

• Published in: Lifetime data analysis Vol. 17; no. 3; pp. 409 - 432
• Main Authors: Stocker, Russell S., Adekpedjou, Akim
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.07.2011; Springer Nature B.V
• Subjects: Air Conditioning - instrumentation; Asymptotic methods; Calendars; Chi-Square Distribution; Data Interpretation, Statistical; Economics; Finance; Health Sciences; Hypotheses; Insurance; Management; Mathematics and Statistics; Medicine; Models, Statistical; Operations Research/Decision Theory; Quality Control; Random variables; Reliability; Safety and Risk; Statistical inference; Statistics; Statistics for Business; Statistics for Life Sciences; Stochastic models; Stochastic Processes; Studies; Survival analysis; Khmaladze’s transformation; Goodness-of-fit tests; Counting processes; Effective age; Martingales; Stochastic integration
• ISSN: 1380-7870; 1572-9249
• DOI: 10.1007/s10985-011-9193-1

A class of tests for the hypothesis that the baseline intensity belongs to a parametric class of intensities is given in the recurrent event setting. Asymptotic properties of a weighted general class of processes that compare the non-parametric versus parametric estimators for the cumulative intensity are presented. These results are given for a sequence of Pitman alternatives. Test statistics are proposed and methods of obtaining critical values are examined. Optimal choices for the weight function are given for a class of chi-squared tests. Based on Khmaladze’s transformation we propose distributional free tests. These include the types of Kolmogorov–Smirnov and Cramér–von Mises. The tests are used to analyze two different data sets.