On constrained smoothing and out-of-range prediction using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si15.svg"><mml:mi>P</mml:mi></mml:math>-splines: A conic optimization approach

• We study the problem of estimating smooth curves which verify structural properties. propose a mathematical optimization formulation to build constrained P-splines. An open-source Python library is developed: cpsplines. estimate in simulated, COVID-19 and demographic data. Decision-making often based on analysis complex evolving Thus, having systems allow incorporate human knowledge provide valuable support decider becomes crucial. In this work, statistical modelling paradigms merge address properties, both observed domain data have been gathered outwards. assume that curve be estimated defined through reduced-rank basis ( B -splines) fitted via penalized splines approach P -splines). To requirements about sign, monotonicity curvature fitting procedure, conic programming developed which, for first time, successfully conveys out-of-range prediction. summary, contributions paper are fourfold: first, estimation non-negative P-splines proposed; second, previous results generalized prediction framework; third, these approaches extended other shape constraints multiple fitting; fourth, an open source cpsplines . use simulated instances, evolution pandemic mortality rates different age groups test our approaches.