Change-point regression with a smooth additive disturbance

We assume a nonparametric regression model where the signal is given by the sum of a piecewise constant function and 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 additive decomposition of the signal when detecting change-points. This is motivated by several applications and by theoretical results about partial linear model. We show how the use of the Epanechnikov kernel in the linear smoother results in very fast computation. Simulations demonstrate that our approach has a small mean squared error and detects change-points well. We also apply the methodology to genome sequencing data to detect copy number variations. Finally, we demonstrate its flexibility by proposing extensions to multivariate and filtered data. An R-package called PCpluS is available on CRAN.