Parameter estimation for differential equations: a generalized smoothing approach
AbstractWe propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus. Copyright 2007 Royal Statistical Society.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Volume (Year): 69 (2007)
Issue (Month): 5 ()
Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Web page: http://www.blackwellpublishing.com/journal.asp?ref=1369-7412
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.
- Pascal Deboeck & Steven Boker, 2010. "Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices," Psychometrika, Springer, vol. 75(3), pages 420-437, September.
- Hong, Zhaoping & Lian, Heng, 2012. "Time-varying coefficient estimation in differential equation models with noisy time-varying covariates," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 58-67, January.
- Nancy Heckman, 2010. "Comments on: Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 19(1), pages 46-49, May.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.