Linear Trend Filtering via Adaptive LASSO
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Linear trend filtering methods are popular due to their overall simplicity—the model is linear in each segment and there are typically only few segments considered. These segments are defined by unique points where the trend changes its direction—so-called changepoints. In this paper, we consider an innovative estimation approach for such models. Our proposal is based on recent developments in the atomic pursuit techniques: we present an estimation algorithm based on the adaptive LASSO penalty and we introduce a fully data-driven method which can be effectively used to fit the continuous linear trend models. Some statistical properties are discussed and the empirical performance is compared with respect to other competitive LASSO-based techniques.
KeywordsLinear trend filtering Joinpoint regression Regularization Lasso Adaptive lasso Changepoints Oracle properties
This work was partially supported by the research grant provided by the Czech Science Foundation, grant number P402/12/G097 and the Mobility Grant provided by the Ministry of Education, Youth and Sports in the Czech Republic, grant number 7AMB17FR030.
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