Classes of Fixed-order and Adaptive Smooth Goodness-of-fit Tests with Discrete Right-censored Data

Classes of hazard-odds based fixed-order and adaptive smooth goodnessof-fit tests for the composite hypothesis that an unknown discrete distribution belongs to a family of distributions using right-censored observations are presented. The proposed classes of tests generalize Neyman’s 33 smooth class of tests. The class of fixed-order tests is the discrete analog of the hazard-based class of tests for continuous failure times studied in Peña. The class of adaptive tests employs a modified Schwartz Bayesian information criterion for choosing the order of the embedding class, with the modification on the criterion accounting for the incompleteness mechanism.