An ordinary differential equation-based solution path algorithm

Yichao Wu

Journal of Nonparametric Statistics, 2011, vol. 23, issue 1, 185-199

Abstract: Efron, Hastie, Johnstone, and Tibshirani [(2004), ‘Least Angle Regression (with discussions)’, The Annals of Statistics, 32, 409–499] proposed least angle regression (LAR), a solution path algorithm for the least squares regression. They pointed out that a slight modification of the LAR gives the LASSO [Tibshirani, R. (1996), ‘Regression Shrinkage and Selection Via the Lasso’, Journal of the Royal Statistical Society, Series B, 58, 267–288] solution path. However, it is largely unknown how to extend this solution path algorithm to models beyond the least squares regression. In this work, we propose an extension of the LAR for generalised linear models and the quasi-likelihood model by showing that the corresponding solution path is piecewise given by solutions of ordinary differential equation (ODE) systems. Our contribution is twofold. First, we provide a theoretical understanding on how the corresponding solution path propagates. Second, we propose an ODE-based algorithm to obtain the whole solution path.

Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1080/10485252.2010.490584 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:23:y:2011:i:1:p:185-199

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485252.2010.490584

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().