Data Dependent Cells Chi‐Square Test With Recurrent Events |
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| Authors: | Akim Adekpedjou WITHANAGE A De Mel Gideon KD Zamba |
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| Affiliation: | 1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA;2. Department of Mathematics and Statistics, Binghamton University, Binghamton, NY 13902, USA;3. Department of Biostatistics, The University of Iowa, Iowa City, IA 52242, USA |
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| Abstract: | We consider a recurrent event wherein the inter‐event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q‐dimensional parameter is unknown. We propose a general Chi‐squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi‐square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures. |
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| Keywords: | Chi‐squared test data dependent cells empirical process minimum chi‐square estimator recurrent events Pitman efficiency |
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