Enhancing Adaptive Spline Regression: An Evolutionary Approach to Optimal Knot Placement and Smoothing Parameter Selection

Standard approaches for nonparametric curve fitting are often too restrictive when trying to estimate covariate effects that feature sudden changes or drastically changing curvature. In this context, adaptive smoothing approaches have received a lot of attention, but are typically limited in their ability to study additive models with multiple covariate effects, the consideration of nonnormal data and/or distributional regression scenarios, and usually rely on either optimizing number and location of knots for the basis functions in nonparametric smoothing or on making the smoothing parameter covariate-dependent. Another inherent problem lies in the independent optimization of knots and smoothing parameters, overlooking the essential interdependence that ensures accurate modeling results. In this article, we propose an approach based on particle swarm optimization that overcomes these limitations and shows very promising performance in complex simulations and applications. Our methodology is adaptable to all types of splines, including univariate and multivariate, and extends to regression techniques beyond the mean, such as models for location, scale and shape and additive quantile regression. The source code is available at https://github.com/AnFreTh/OKPSPS. Supplementary materials for this article are available online.