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Spline regression with automatic knot selection

Author

Listed:
  • Goepp, Vivien
  • Bouaziz, Olivier
  • Nuel, Grégory

Abstract

Spline regression has proven to be a useful tool for nonparametric regression. The flexibility of this function family is based on basepoints defining shifts in the behavior of the function – called knots. The question of setting the adequate number of knots and their placement is usually overcome by penalizing over the spline's overall smoothness (e.g. P-splines). However, there are areas of application where finding the best knot placement is of interest. A new method is introduced for automatically selecting knots in spline regression. The approach consists in setting many initial knots and fitting the spline regression through a penalized likelihood procedure called adaptive ridge, which discards the least relevant knots. The method – called A-splines, for adaptive splines – compares favorably with other knot selection methods: it runs way faster (∼10 to ∼400 faster) than comparable methods and has close to equal predictive performance. A-splines are applied to both simulated and real datasets.

Suggested Citation

  • Goepp, Vivien & Bouaziz, Olivier & Nuel, Grégory, 2025. "Spline regression with automatic knot selection," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001270
    DOI: 10.1016/j.csda.2024.108043
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