• Asymptotic distribution;
  • Changepoint;
  • Conditional inference

Summary Maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures. This powerful framework contains most of the published procedures in this area as special cases, such as maximally selected χ2 and rank statistics, but also allows for direct construction of new test procedures for less standard test problems. As an application, a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions. This new test is employed to search for a high-risk group of rectal cancer patients treated with a neo-adjuvant chemoradiotherapy. Moreover, a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints.