2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166470We 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)Statistics Theory62G07, 62G10, 62G15, 62G20, 62G30 (Primary)text