minimalIntervals: Compute set of minimal intervals

In modehunt: Multiscale Analysis for Density Functions

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, [e-mail],
http://www.kasparrufibach.ch

Guenther Walther, [e-mail],
https://gwalther.su.domains/

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.

modehunt documentation built on June 8, 2025, 9:38 p.m.