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We propose Robust Narrowest Significance Pursuit (RNSP), a methodology fordetecting localized regions in data sequences which each must contain achange-point in the median, at a prescribed global significance level. RNSPworks by fitting the postulated constant model over many regions of the datausing a new sign-multiresolution sup-norm-type loss, and greedily identifyingthe shortest intervals on which the constancy is significantly violated. Byworking with the signs of the data around fitted model candidates, RNSP fulfilsits coverage promises under minimal assumptions, requiring only sign-symmetryand serial independence of the signs of the true residuals. In particular, itpermits their heterogeneity and arbitrarily heavy tails. The intervals ofsignificance returned by RNSP have a finite-sample character, are unconditionalin nature and do not rely on any assumptions on the true signal. Codeimplementing RNSP is available at https://github.com/pfryz/nsp.

Robust Narrowest Significance Pursuit: Inference for multiple change-points in the median