Abstract
Joinpoint regression models are very popular in some practical areas mainly due to a very simple interpretation which they offer. In some situations, moreover, it turns out to be also useful to require some additional qualitative prop- erties for the final model to be satisfied.
Especially properties related to the mono- tonicity of the fit are of the main interest in this paper. We propose a LASSO regular- ized approach to estimate these types of models where the optional shape constraints can be implemented in a straightforward way as a set of linear inequalities and they are considered simultaneously within the estimation process itself.
As the main result we derive a testing approach which can be effectively used to statistically verify the validity of the imposed shape restrictions in piecewise linear continuous models. We also investigate some finite sample properties via a simula- tion study.