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This covers the common situation that either the baseline-level or additional parameters such as the variance are unknown and have to be estimated from the data. We argue that state of the art approaches to determine asymptotically correct critical values for multiscale scanning statistics will in general fail when such parameters are naively replaced by plug-in estimators. Instead, we suggest to estimate the nuisance parameters on the largest scale and to use (only) smaller scales for multiscale scanning. We prove a uniform invariance principle for the resulting adjusted multiscale statistic, which is widely applicable and provides a computationally feasible way to simulate asymptotically correct critical values. We illustrate the implications of our theoretical results in a simulation study and in a real data example from super-resolution STED microscopy. This allows us to identify interesting regions inside a specimen in a pre-scan with controlled family-wise error rate.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae100","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T18:45:03Z","timestamp":1729536303000},"page":"510-528","source":"Crossref","is-referenced-by-count":0,"title":["Multiscale scanning with nuisance parameters"],"prefix":"10.1093","volume":"87","author":[{"given":"Claudia","family":"K\u00f6nig","sequence":"first","affiliation":[{"name":"Institute for Mathematical Stochastics, University of G\u00f6ttingen , G\u00f6ttingen ,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Axel","family":"Munk","sequence":"additional","affiliation":[{"name":"Institute for Mathematical Stochastics, University of G\u00f6ttingen , G\u00f6ttingen ,","place":["Germany"]},{"name":"DFG Cluster of Excellence \u2018Multiscale Bioimaging - From Molecular Machines to Networks of 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