In general, all intervals that have a test statistic bigger than the respective critical value are output. For a given set of intervals \(\mathcal{K}\), all intervals \(J\) such that \(\mathcal{K}\) does not contain a proper subset of \(J\) are called minimal. Given \(\mathcal{K}\), this function computes the set of minimal intervals.
minimalIntervals(ints)Returns the set of minimal elements \(\bf{D}^\pm\), corresponding to the set of input intervals
\(\mathcal{D}^\pm\).
Either one of the sets \(\mathcal{D}^+\) or \(\mathcal{D}^-\) as output by one of the functions
modeHunting, modeHuntingApprox, or modeHuntingBlock.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
Guenther Walther, gwalther@stanford.edu,
https://gwalther.su.domains/
Minimal intervals were first introduced (although for a different multiscale procedure) on p. 517 in
Lutz Dümbgen (2002). Application of Local Rank Tests to Nonparametric Regression. Journal of Nonparametric Statistics, 14, 511--537.
Rufibach, K. and Walther, G. (2010). A general criterion for multiscale inference. J. Comput. Graph. Statist., 19, 175--190.