Shape-constrained functional regression with penalized splines

M. Durbán, V. Guerrero, C. Molero-Río, J. Secilla Martínez

Functional regression refers to regression models involving functional covariates and/or a functional response. Often, prior knowledge about the relationship between the covariates and the response – arising from biological, medical, or engineering processes - requires that the estimated functional coefficients meet specific shape constraints, such as non negativity, monotonicity or convexity/concavity. However, these requirements are not straightforwardly satisfied when using an unconstrained estimation approach. In this work, we investigate whether the combination of conic optimization and penalized splines (P splines) developed by Navarro-García, Guerrero and Durbán (2023) can outperform recent approaches in the literature for estimating shape-constrained functional regression coefficients. The comparison will be carried out using both simulated and real datasets.

Keywords: Functional regression; Conic optimization; P-splines

AMC2 Robust Methods
June 10, 2025  5:10 PM
Auditorio 1. Ricard Vinyes

E. Boj del Val, A. Grané

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