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A simultaneous changepoint detection and estimation in a piece-wise constant model is a common task in modern statistics. If, in addition, the whole estimation can be performed fully automatically in a single step without requiring any statistical tests or a posteriori methods, it also becomes a very interesting but challenging idea. In this paper, we introduce the estimation method based on the quantile LASSO approach. Unlike standard LASSO approaches, our method does not rely on classical assumptions common for the model errors, sub-Gaussian or Normal distributions in particular. The quantile LASSO method can handle, for instance, outlying observations or heavy-tailed error distributions, and it provides, in general, a more complex insight into the data: any conditional quantile can be obtained rather than providing just the conditional mean. Under some reasonable assumptions, the number of changepoints is not underestimated with probability tenting to one. Moreover, if the number of changepoints is estimated correctly, the quantile LASSO changepoint estimators are consistent. Numerical simulations demonstrate the theoretical results, and they illustrate the empirical performance and the robust favor of the proposed quantile LASSO method. The real example is used to show a practical applicability of the proposed method.

Changepoint Detection by the Quantile LASSO Method