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modehunt (version 1.0.7)

minimalIntervals: Compute set of minimal intervals

Description

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.

Usage

minimalIntervals(ints)

Arguments

ints
Either one of the sets $\mathcal{D}^+$ or $\mathcal{D}^-$ as output by one of the functions modeHunting, modeHuntingApprox, or modeHuntingBlock.

Value

$\bf{D}^\pm$, corresponding to the set of input intervals $\mathcal{D}^\pm$.

References

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.