LEAST-SQUARES ESTIMATION OF A STEP FUNCTION

By Yi-Ching Yao, S. Au. 2016

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A review of change point detection methods (2018, methodology): “First introduced in [68] and later in [134, 135], it was then studied under more general assumptions [24–26].”
Wild binary segmentation for multiple change-point detection (2014, background): “Boysen et al. (2009) use the least-squares criterion with a linear penalty on the number of change-points and, under the assumption of a ﬁnite but arbitrary N , show various theoretical results including analogues of those of Yao and Au (1989).”
A MOSUM procedure for the estimation of multiple random change points (2018, methodology): “More recently, approaches based on least squares ([44] in context of mean changes or [30] for multivariate regression models), least absolute deviations ([7] for mean and simultaneous variance changes or [3] for linear regression models) or the minimum description length (confer [13] for linear auto”
A robust approach for estimating change-points in the mean of an AR(1) process (2014, background): “Observe that, similarly to most of the papers dedicated to multiple change-points estimation [3,21,38], we assume that the number of change-points m is fixed and does not depend on the number of observations.”
Selective review of offline change point detection methods (2020, background): “The penalty function pen AIC ,L 2 is given by en AIC ,L 2 (T ) := σ 2 |T | .”