Generalized Cramér-von Mises tests of goodness of fit for doubly censored data |
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Authors: | Jian-Jian Ren |
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Affiliation: | (1) Division of Statistics, Department of Mathematics and Statistics, University of Nebraska-Lincoln, 810 Oldfather Hall, P.O. Box 880323, 86588-0323 Lincoln, NE, USA |
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Abstract: | We generalize Cramér-von Mises statistics to test the goodness of fit of a lifetime distribution when the data are doubly censored. We derive the limiting distributions of our test statistics under the null hypothesis and the alternative hypothesis, respectively. We also give a strong consistent estimator for the asymptotic covariance of the self-consistent estimator for the survival function with doubly censored data. Thereby, a method, called the Fredholm Integral Equation method, is proposed to estimate the null distribution of test statistics. In this work, the perturbation theory for linear operators plays an important role, and some numerical examples are included.The author's research was supported by a Faculty Fellowship of University of Nebraska-Lincoln. |
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Keywords: | Cramé r-von Mises statistic doubly censored data test of goodness of fit limiting distribution self-consistent estimator survival functions |
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