Representation theorem for convex nonparametric least squares
Timo Kuosmanen ()
Econometrics Journal, 2008, vol. 11, issue 2, 308-325
We examine a nonparametric least-squares regression model that endogenously selects the functional form of the regression function from the family of continuous, monotonic increasing and globally concave functions that can be nondifferentiable. We show that this family of functions can be characterized without a loss of generality by a subset of continuous, piece-wise linear functions whose intercept and slope coefficients are constrained to satisfy the required monotonicity and concavity conditions. This representation theorem is useful at least in three respects. First, it enables us to derive an explicit representation for the regression function, which can be used for assessing marginal properties and for the purposes of forecasting and ex post economic modelling. Second, it enables us to transform the infinite dimensional regression problem into a tractable quadratic programming (QP) form, which can be solved by standard QP algorithms and solver software. Importantly, the QP formulation applies to the general multiple regression setting. Third, an operational computational procedure enables us to apply bootstrap techniques to draw statistical inference. Copyright © 2008 The Author. Journal compilation © Royal Economic Society 2008
References: Add references at CitEc
Citations View citations in EconPapers (33) Track citations by RSS feed
Downloads: (external link)
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1368-423X.2008.00239.x link to full text (text/html)
Access to full text is restricted to subscribers.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: http://EconPapers.repec.org/RePEc:ect:emjrnl:v:11:y:2008:i:2:p:308-325
Ordering information: This journal article can be ordered from
Access Statistics for this article
Econometrics Journal is currently edited by Richard J. Smith, Oliver Linton, Pierre Perron, Jaap Abbring and Marius Ooms
More articles in Econometrics Journal from Royal Economic Society Contact information at EDIRC.
Series data maintained by Wiley-Blackwell Digital Licensing ().