Jump-detection and curve estimation methods for discontinuous regression functions based on the piecewise B-spline function

Liu, Guoxiang; Wang, Mengmeng; Du, Xin; Lin, Jin-Guan; Gao, Qibing

doi:10.1080/03610926.2017.1400061

Cited by 3 publications

(2 citation statements)

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“…all derivatives may change abruptly at a change-point location. Both models were considered in various papers by several approaches, mostly from the perspective of extending smoothing approaches, such as kernel regression (Müller, 1992;Qiu, 1994;Eubank and Speckman, 1994;Qiu, 2003;Gijbels and Goderniaux, 2004), local polynomial regression (Loader, 1996;Spokoiny, 1998;Gijbels et al, , 2007Mboup et al, 2008;Xia and Qiu, 2015;Zhang, 2016), (smoothing) splines (Koo, 1997;Lee, 2002;Miyata and Shen, 2003;Huang and Qiu, 2010;Yang and Song, 2014;Liu et al, 2018), wavelet (Raimondo, 1998;Antoniadis and Gijbels, 2002;Abramovich et al, 2007) and Bayesian (Denison et al, 1998;Ogden, 1999;DiMatteo et al, 2001;Punskaya et al, 2002;Fearnhead, 2005;Moreno et al, 2013; approaches. A helpful review is given in (Qiu, 2005).…”

Section: Related Workmentioning

confidence: 99%

“…In many applications however, while the signal h may change abruptly, between these change-points the signal may not be precisely constant. Examples in the literature are from climatology (Qiu and Yandell, 1998;Qiu, 2003;Wu and Zhao, 2007), finance (Wang, 1995;Gijbels et al, 2007;Lam et al, 2016;Liu et al, 2018), light transmittance (Abramovich et al, 2007) and many more. Instead, many works assume (see Section 1.1) that…”

Section: Introductionmentioning

confidence: 99%

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Change-point regression with a smooth additive disturbance

Pein¹

2021

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We assume a nonparametric regression model with signals given by the sum of a piecewise constant function ands a smooth function. To detect the change-points and estimate the regression functions, we propose PCpluS, a combination of the fused Lasso and kernel smoothing. In contrast to existing approaches, it explicitly uses the assumption that the signal can be decomposed into a piecewise constant and a smooth function when detecting change-points. This is motivated by several applications and by theoretical results about partial linear model. Tuning parameters are selected by cross-validation. We argue that in this setting minimizing the L 1 -loss is superior to minimizing the L 2 -loss. We also highlight important consequences for cross-validation in piecewise constant change-point regression. Simulations demonstrate that our approach has a small average mean square error and detects change-points well, and we apply the methodology to genome sequencing data to detect copy number variations. Finally, we demonstrate its flexibility by combining it with smoothing splines and by proposing extensions to multivariate and filtered data.

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