Testing Shape Constraints in Lasso Regularized Joinpoint Regression
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 properties for the final model to be satisfied. Especially properties related to the monotonicity of the fit are of the main interest in this paper. We propose a LASSO regularized 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 simulation study.
KeywordsJoinpoint regression Regularization Shape constraints Post-selection inference
We thank Ivan Mizera, Sen Bodhisattva and the referee for their comments and remarks. This work was partially supported by the PRVOUK grant 300-04/130.
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