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 problem of interest is to make inference about the distribution of the event occurrence time. In this talk some tests of goodness-of-fit hypothesis pertaining to this distribution based on certain marked empirical processes will be discussed. In the case of simple hypothesis, these tests are asymptotically distribution-free. When fitting a parametric model, the null weak limit of this process is a Gaussian process with a covariance function depending on the null model. A Stute-Thies-Zhu type transformed version of the process is shown to converges weakly to a continuous time transformed Brownian motion. The tests based on this process are thus asymptotically distribution-free. The proposed tests are shown to be 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 good finite sample level preservation and power behavior.
Group for Research in Decision Analysis