Knot selection for least-squares and penalized splines

Two new stochastic search methods are proposed for optimizing the knot locations and/or smoothing parameters for least-squares or penalized splines. One of the methods is a golden-section-augmented blind search, while the other is a continuous genetic algorithm. Monte Carlo experiments indicate that the algorithms are very successful at producing knot locations and/or smoothing parameters that are near optimal in a squared error sense. Both algorithms are amenable to parallelization and have been implemented in OpenMP and MPI. An adjusted GCV criterion is also considered for selecting both the number and location of knots. The method performed well relative to MARS in a small empirical comparison.