From smoothing splines to generalized penalized splines: Structure and rates of convergence

Ioannis Kalogridis (University of Glasgow)

Tuesday 12th May 12:00-13:00
Maths 311B

Abstract

Penalized splines (P-splines) have been indispensable in nonparametric regression for over 40 years, valued for their combination of flexibility and computational efficiency. Yet their hybrid nature - blending finite-dimensional approximations with a continuous penalty – delayed a full theoretical understanding for many years, and only recently has a clear picture begun to emerge. In this talk, I retrace the historical evolution of splines in Statistics and present penalized splines as a practical solution to the challenges faced by earlier estimation methods, such as computational scalability and instability. I discuss recent theoretical breakthroughs, including convergence rates and variance-bias decompositions, and show how these results clarify the roles of the number of knots and the smoothing parameter, settling long-standing questions. These concepts have broad applicability across different areas including survival, longitudinal, functional, and spatial data analysis.

 

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