minimalIntervals {modehunt}R Documentation

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

Returns the set of minimal elements bf{D}^pm, corresponding to the set of input intervals mathcal{D}^pm.

Note

Depending on the value of min.int, this function is called by modeHunting,
modeHuntingApprox, and modeHuntingBlock.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

Guenther Walther, gwalther@stanford.edu,
www-stat.stanford.edu/~gwalther

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. (2007). A general criterion for multiscale inference. Preprint, Department of Statistics, Stanford University.


[Package modehunt version 1.0.4 Index]