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Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.<\/jats:p>","DOI":"10.1111\/rssb.12322","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T04:12:42Z","timestamp":1559275962000},"page":"649-672","source":"Crossref","is-referenced-by-count":114,"title":["Narrowest-Over-Threshold Detection of Multiple Change Points and Change-Point-Like Features"],"prefix":"10.1093","volume":"81","author":[{"given":"Rafal","family":"Baranowski","sequence":"first","affiliation":[{"name":"London School of Economics and Political Science \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yining","family":"Chen","sequence":"additional","affiliation":[{"name":"London School of Economics and Political Science \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piotr","family":"Fryzlewicz","sequence":"additional","affiliation":[{"name":"London School of Economics and Political Science \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,5,30]]},"reference":[{"key":"2023022002403597600_","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S0092-8240(89)80047-3","article-title":"Algorithms for the optimal identification of segment neighborhoods","volume":"51","author":"Auger","year":"1989","journal-title":"Bull. 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