Chi-Squared Goodness of Fit Test Based on Random Cells with Recurrent
Withanage De Mel
Missouri University of Science and Technology
Akim Adekpedjou
Missouri University of Science and Technology
Gideon Zamba
University of Iowa
We consider a recurrent event wherein the inter-event time distribution F is assumed to belong to some parametric family of the distributions F, where the unknown parameter is q-dimensional. This work deals with the problem of goodness-of-fit test for F. We develop a chi-square type test where the k nonoverlapping cell boundaries are randomly chosen. Our test used a Kaplan Meier type nonparametric maximum likelihood estimator (NPMLE) of F to obtain the observed frequencies. The minimum distance estimator of is obtained by minimizing the quadratic form that resulted from the properly scaled vector of differences between the observed and expected cell frequencies. The proposed chi-square test statistic is constructed by using the NPMLE of F and the minimum distance estimator. We show that the proposed test statistic is asymptotically chi-square with k-q-1 degrees of freedom. Results for specific families of distributions such as Weibull is presented. We also discuss results of a simulation study as well as application to a biomedical data set.