Multiscale inference about a density

Abstract

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.

Version 2 is an extended version (Technical report 56, IMSV, Univ. Bern) which is referred to in version 3. Published in at http://dx.doi.org/10.1214/07-AOS521 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Multiscale inference about a density
• Densities, spectral densities and modality
• Testing for monotone increasing hazard rate

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