A Generalized Chi-Square Goodness-of-Fit Test for Recurrent Failure Time Data

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Withanage De Mel and Akim Adekpedjou*+ and Gideon K.D. Zamba
• Companies: Missouri University of Science and Technology and Missouri University of Science and Technology and University of Iowa
• Keywords: Recurrent Failure ; Goodness of Fit ; Minimum Distance Estimator ; Gaussian Process ; Composie hypotheses

Abstract

The problem of goodness of fit of the distribution function F governing the time to occurrence of a recurrent event is considered. Specifically, we develop a test for the null hypothesis that F belongs to some parametric family \mathcal{F}(t, \theta}. We derive a generalization of the chi-square goodness of fit (Pearson-like) test based on a nonparametric maximum likelihood estimator of F which possesses asymptotic properties such as consistency and convergence to Gaussian processes. The parameter \theta is estimated by the value that minimizes the distance between the vector of observed and expected frequency over k non-overlapping partitions. We prove that the test statistic is asymptotically chi-square distributed. We provide results of a simulation study and application to real recurrent failure time data.