NDLI: Estimation of shape constrained functions in dynamical systems and its application to gene networks

Content Provider	IEEE Xplore Digital Library
Author	Jinglai Shen Xiao Wang
Copyright Year	2010
Description	Author affiliation: Dept. of Stat., Purdue Univ., West Lafayette, IN, USA (Xiao Wang) \|\| Dept. of Math. & Stat., Univ. of Maryland Baltimore County, Baltimore, MD, USA (Jinglai Shen)
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.
Starting Page	5948
Ending Page	5953
File Size	486267
Page Count	6
File Format	PDF
ISBN	9781424474264
ISSN	07431619
e-ISBN	9781424474271
DOI	10.1109/ACC.2010.5531240
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-06-30
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Spline Systems engineering and theory State estimation Filtering Biomedical measurements Shape control Control systems Statistical distributions Noise measurement Biological control systems
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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