Abstract: We propose a dynamic version of the penalized spline regression designed for streaming data that allows for the insertion of new knots dynamically based on sequential updates of the summary statistics. A new theory using direct functional methods rather than the traditional matrix analysis is developed to attain the optimal convergence rate in the L² sense for the dynamic estimation (also applicable for standard penalized splines) under weaker conditions than those in existing works on standard penalized splines.

Key words and phrases: Convergence rate, nonparametric regression, streaming data.