Representation theorem for convex nonparametric least squares
AbstractWe 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
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 Economic Society in its journal Econometrics Journal.
Volume (Year): 11 (2008)
Issue (Month): 2 (07)
Contact details of provider:
Postal: Office of the Secretary-General, School of Economics and Finance, University of St. Andrews, St. Andrews, Fife, KY16 9AL, UK
Phone: +44 1334 462479
Web page: http://www.res.org.uk/
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Andor, Mark & Hesse, Frederik, 2012. "The StoNED age: The departure into a new era of efficiency analysis? An MC study comparing StoNED and the "oldies" (SFA and DEA)," CAWM Discussion Papers 60, Center of Applied Economic Research Münster (CAWM), University of Münster.
- Johnson, Andrew L. & Kuosmanen, Timo, 2012. "One-stage and two-stage DEA estimation of the effects of contextual variables," European Journal of Operational Research, Elsevier, vol. 220(2), pages 559-570.
- Kortelainen, Mika, 2008. "Estimation of semiparametric stochastic frontiers under shape constraints with application to pollution generating technologies," MPRA Paper 9257, University Library of Munich, Germany.
- Timo Sipil�inen & Anni Huhtala, 2013.
"Opportunity costs of providing crop diversity in organic and conventional farming: would targeted environmental policies make economic sense?,"
European Review of Agricultural Economics,
Foundation for the European Review of Agricultural Economics, vol. 40(3), pages 441-462, July.
- Sipilainen, Timo & Huhtala, Anni, 2011. "Opportunity Costs of Providing Crop Diversity in Organic and Conventional Farming: Would Targeted Environmental Policies Make Economic Sense?," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114527, European Association of Agricultural Economists.
- Mekaroonreung, Maethee & Johnson, Andrew L., 2012. "Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach," Energy Economics, Elsevier, vol. 34(3), pages 723-732.
- Timo Kuosmanen & Mogens Fosgerau, 2009.
"Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals,"
Scandinavian Journal of Economics,
Wiley Blackwell, vol. 111(2), pages 351-367, 06.
- Kuosmanen, Timo & Fosgerau, Mogens, 2009. "Neoclassical versus frontier production models? Testing for the skewness of regression residuals," MPRA Paper 24208, University Library of Munich, Germany.
- Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150289, Agricultural and Applied Economics Association.
- Kuosmanen, Timo, 2012. "Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model," Energy Economics, Elsevier, vol. 34(6), pages 2189-2199.
- Lee, Chia-Yen & Johnson, Andrew L. & Moreno-Centeno, Erick & Kuosmanen, Timo, 2013. "A more efficient algorithm for Convex Nonparametric Least Squares," European Journal of Operational Research, Elsevier, vol. 227(2), pages 391-400.
- Andrew Johnson & Timo Kuosmanen, 2011. "One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method," Journal of Productivity Analysis, Springer, vol. 36(2), pages 219-230, October.
- Mark Andor & Frederik Hesse, . "The StoNED age: The Departure Into a New Era of Efficiency Analysis? An MC study Comparing StoNED and the "Oldies" (SFA and DEA)," Working Papers 201285, Institute of Spatial and Housing Economics, Munster Universitary.
- Sipilainen, Timo & Kuosmanen, Timo & Kumbhakar, Subal C., 2008. "Measuring productivity differentials – An application to milk production in Nordic countries," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44277, European Association of Agricultural Economists.
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.