Inference in dynamic systems using B‐splines and quasilinearized ODE penalties. Issue 3 (25th November 2015)

• Record Type: Journal Article
• Authors: Frasso, Gianluca; Jaeger, Jonathan; Lambert, Philippe
• Is Part Of: Biometrical journal. Volume 58:Issue 3(2016:May)
• Page Start: 691
• Page End: 714
• Publication Date: 2015-11-25
• Subjects: Nonlinear ordinary differential equations -- Penalized splines -- Quasilinearization; Biometry -- Periodicals; Medical statistics -- Periodicals; 570.15195
• DOI: 10.1002/bimj.201500082
• Languages: English
• ISSNs: 0323-3847

Abstract

Abstract : Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one‐dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE‐based penalty. Within the quasilinearized spline‐based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known.