Constructing Spline State Space Models from Generalized Taylor Expansions

• Activity Number: 106 - New Statistical Models for Functional Data/ Longitudinal Data
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mengying You* and Wensheng Guo
• Companies: University of Pennsylvania and University of Pennsylvania
• Keywords: semiparametric state space models; smoothing splines; generalized Taylor expansions

Abstract

Smoothing splines have a wide range of applications because of their flexibility to incorporate prior information through construction of the reproducing kernel Hilbert space corresponding to the penalty. The general fitting algorithms are computationally intensive because these algorithms usually require inversions of large dimensional matrices. Constructing state space models for smoothing splines would enable adopting existing O(n) Kalman filtering and smoothing algorithms to estimate the smoothing parameter and regression function. Current state space models for smoothing splines are mainly limited to polynomial splines. In this article, we propose to construct equivalent state space models for general smoothing splines. Our construction is explicit and unified. The construction not only provides a computationally efficient way for fitting smoothing splines, but also leads to a large class of semiparametric state space models for signal extraction and forecasting.