Goodness-of-fit testing in interval censoring case 1

In the interval censoring case 1, an event occurrence time is unobservable, but one observes an inspection time and whether the event has occurred prior to this time or not. The focus here is to provide tests of goodness-of-fit hypothesis pertaining to the distribution of the event occurrence time. The proposed tests are based on certain marked empirical processes for testing a simple hypothesis and the Stute–Thies–Zhu transformation of such a process for fitting a parametric family of distributions. These tests are asymptotically distribution-free, consistent against a large class of fixed alternatives and have nontrivial asymptotic power against a large class of local alternatives. A simulation study is included to exhibit the finite sample level preservation and power behavior.