Generalized Maximally Selected Statistics

Torsten Hothorn, Achim Zeileis

Publication: Working/Discussion PaperWU Working Paper

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Abstract

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 chi-squared 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.

Publication series

SeriesResearch Report Series / Department of Statistics and Mathematics
Number52

WU Working Paper Series

  • Research Report Series / Department of Statistics and Mathematics

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