Title :
Estimation of shape constrained functions in dynamical systems and its application to gene networks
Author :
Jinglai Shen ; Xiao Wang
Author_Institution :
Dept. of Math. & Stat., Univ. of Maryland Baltimore County, Baltimore, MD, USA
fDate :
June 30 2010-July 2 2010
Abstract :
Inspired by estimation and identification of biological and engineering systems subject to constraints, this paper addresses nonparametric estimation of monotone functions contained in a class of dynamical systems. A two-stage estimation procedure is proposed. At the first stage, partial state estimation is performed via trend filtering techniques. At the second stage, a penalized spline (or P-spline for short) estimator is used to estimate monotone functions. The highlight of the paper is asymptotic analysis of the monotone P-spline estimator formulated as a constrained optimization problem. The uniform Lipschitz property is established for optimal spline coefficients. By approximating the estimator by a solution of a differential equation with a constrained right-hand side, the paper develops asymptotic normality at interior points and establishes convergence rates. The proposed estimator is applied to estimation of a monotone regulatory function in a gene regulatory network.
Keywords :
differential equations; estimation theory; identification; optimisation; splines (mathematics); asymptotic analysis; asymptotic normality; biological system; constrained optimization problem; differential equation; dynamical system; engineering system; gene regulatory network; monotone P-spline estimator; monotone function; monotone regulatory function; nonparametric estimation; optimal spline coefficient; partial state estimation; penalized spline estimator; shape constrained function; trend filtering technique; uniform Lipschitz property; Biological control systems; Biomedical measurements; Control systems; Filtering; Noise measurement; Shape control; Spline; State estimation; Statistical distributions; Systems engineering and theory;
Conference_Titel :
American Control Conference (ACC), 2010
Conference_Location :
Baltimore, MD
Print_ISBN :
978-1-4244-7426-4
DOI :
10.1109/ACC.2010.5531240