A short note on model selection by LASSO methods in a change-point model

In Ciuperca (2012) (Ciuperca. Model selection by LASSO methods in a change-point model, Stat. Papers, 2012; (in press)), the author considered a linear regression model with multiple change-points occurring at unknown times. In particular, the author studied the asymptotic properties of the LASSO-type and of the adaptive LASSO estimators. While the established results seem interesting, we point out some major errors in proof of the most important result of the quoted paper. Further, we present a corrected result and proof.