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Activity Number: 77
Type: Contributed
Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
Sponsor: Biometrics Section
Abstract - #307629
Title: Chi-Squared Goodness of Fit Test Based on Random Cells with Recurrent Event Data
Author(s): Withanage De Mel*+ and Akim Adekpedjou and Gideon K.D. Zamba
Companies: Missouri S&T and Missouri University of Science and Technology and University of Iowa
Keywords: Recurrent Events ; Chi-square Test ; Random Cells Boundaries ; Minimum Chi-Square Estimator
Abstract:

We consider a recurrent event wherein the inter-event time distribution $F$ is assumed to belong to some parametric family of the distributions $\mathcal{F},$ where the unknown parameter $\theta$ 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 $\theta$ 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 and Exponential are presented. We also discuss results of a simulation study as well as application to a biomedical data set.


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