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GENERALIZED CRAMÉR-VON MISES TESTS OF GOODNESS

OF FIT FOR DOUBLY CENSORED DATA

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JIAN-JIAN REN

*Division of Statistics, Department of Mathematics and
Statistics,*

University of Nebraska-Lincoln, 810 Oldfather Hall,

P.O. Box 880323, Lincoln, NE 86588-0323, U.S.A.
(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.

**Source**
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