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Generalized Maximally Selected Statistics
Author(s) -
Hothorn Torsten,
Zeileis Achim
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2008.00995.x
Subject(s) - statistics , categorical variable , mathematics , statistic , rank (graph theory) , test statistic , inference , statistical hypothesis testing , wilcoxon signed rank test , computer science , artificial intelligence , combinatorics , mann–whitney u test
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 χ 2 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.