# minimalIntervals: Compute set of minimal intervals In modehunt: Multiscale Analysis for Density Functions

## 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

 1 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,
http://www.kasparrufibach.ch

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. (2010). A general criterion for multiscale inference. J. Comput. Graph. Statist., 19, 175–190.

modehunt documentation built on May 2, 2019, 3:31 a.m.