title: Inference in dynamic systems using B-splines and quasilinearized ODE penalties.
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.
authors.affiliation: Faculté des Sciences Sociales, Méthodes Quantitatives en Sciences Sociales, Université de Liège, Boulevard du Rectorat 7, B-4000, Liège, Belgium.
authors.forename: Gianluca
authors.initials: G
authors.lastname: Frasso
authors.affiliation: Nestlé Research Center, Lausanne, Switzerland.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Jaeger
authors.affiliation: Faculté des Sciences Sociales, Méthodes Quantitatives en Sciences Sociales, Université de Liège, Boulevard du Rectorat 7, B-4000, Liège, Belgium.|Institut de Statistique, Biostatistique et Sciences Actuarielles, Université Catholique de Louvain, Belgium.
authors.forename: Philippe
authors.initials: P
authors.lastname: Lambert
mesh_terms: D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D016018:Least-Squares Analysis; D015233:Models, Statistical
keywords: Nonlinear ordinary differential equations; Penalized splines; Quasilinearization