A Chi-Squared Goodness-of-Fit Test for Randomly Censored Data

In this article, procedures analogous to Karl Pearson's well-known chi-squared goodness-of-fit test for a simple null hypothesis are developed under the random censorship model. It is shown that one straightforward analog of Pearson's statistic is diminished in applicability due to the form of its limiting distribution. This leads to the development of an asymptotically exact test based on a Wald-type statistic with a chi-squared limiting null distribution. This test is compared and contrasted theoretically and via a simulation with Akritas’ test with respect to significance levels, asymptotic local powers, and finite sample powers. The general conclusions from the simulation study are that the proposed test usually achieves the desired significance levels when the probability of observing a censored or an uncensored value in the last interval is not small, whereas Akritas’ test tends to be a bit anticonservative. On the other hand, Akritas’ test is more powerful than the proposed test in a model with Weibull lifetimes, but in models with exponential and normal lifetimes neither test dominates the other.