On the use of P-splines for constrained smoothing and out-of-range prediction
M. Navarro-García, V. Guerrero, M. Durbán
In an era when the decision-making process is often based on the analysis of complex and evolving data, it is crucial to have systems which allow to incorporate human knowledge and provide valuable support to the decider. In this work, statistical modelling and mathematical optimization paradigms merge to address the problem of estimating smooth curves and hypersurfaces which verify structural properties, both in the observed domain in which data have been gathered and outwards. We assume that the smooth hypersurface to be estimated is defined through a reduced-rank basis (B−splines) and fitted via a penalized splines approach (P−splines). To incorporate shape requirements in the fitting procedure, a conic optimization model is stated and solved which, for the first time, successfully conveys out-of-range constrained forecasting. This approach is successfully applied to simulated and demographic data, as well as to data arising in the context of the COVID-19 pandemic.
Keywords: P-splines, Conic Optimization, Smoothing, Prediction
Scheduled
GT04 Multivariate Analysis and Classification V. Mathematical Optimization and Data Science
June 8, 2022 12:40 PM
Cloister room
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N. Gómez-Vargas, R. Blanquero, E. Carrizosa
S. Pineda, M. Á. Muñoz, J. M. Morales González
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6/8/22
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