Abstract
Piece-wise linear models are quite popular real applications because of their overall simplicity and straightforward interpretation. In addition, such models are quite flexible in terms of their ability to adapt to existing changes in the trend which usually models the underlying time dependent structure.
In this paper we propose an innovative ap- proach to the linear trend filtering which is based on the sparsity princi- ple in atomic pursuit estimation via an adaptive LASSO approach. The proposed method is oracle consistent and the final estimate can be con- structed with the same time efficiency as an ordinary linear regression.
Moreover, one can take a full advantage of many efficient algorithms used to fit standard LASSO problems. We present some theoretical properties and the finite sample performance is investigated using a comparative simulation study.