(Received February 16, 1994; revised December 12, 1994)
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.
Key words and phrases: Cramér-von Mises statistic, doubly censored data, test of goodness of fit, limiting distribution, self-consistent estimator, survival functions.