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Smoothing: Local Regression Techniques

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  • Loader, Catherine

Abstract

Smoothing methods attempt to find functional relationships between different measurements. As in the standard regression setting, the data is assumed to consist of measurements of a response variable, and one or more predictor variables. Standard regression techniques (Chapter ??) specify a functional form (such as a straight line) to describe the relation between the predictor and response variables. Smoothing methods take a more flexible approach, allowing the data points themselves to determine the form of the fitted curve. This article begins by describing several different approaches to smoothing, including kernel methods, local regression, spline methods and orthogonal series. A general theory of linear smoothing is presented, which allows us to develop methods for statistical inference, model diagnostics and choice of smoothing parameters. The theory is then extended to more general settings, including multivariate smoothing and likelihood models.

Suggested Citation

  • Loader, Catherine, 2004. "Smoothing: Local Regression Techniques," Papers 2004,12, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    • Handle: RePEc:zbw:caseps:200412
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    1. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    2. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
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    1. Hupfeld, Stefan, 2009. "Rich and healthy--better than poor and sick?: An empirical analysis of income, health, and the duration of the pension benefit spell," Journal of Health Economics, Elsevier, vol. 28(2), pages 427-443, March.
    2. Essama-Nssah, B., 2006. "Propensity score matching and policy impact analysis - a demonstration in EViews," Policy Research Working Paper Series 3877, The World Bank.
    3. Conti, Pier Luigi & Marella, Daniela & Scanu, Mauro, 2008. "Evaluation of matching noise for imputation techniques based on nonparametric local linear regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 354-365, December.
    4. Stefan Hupfeld, 2011. "Non-monotonicity in the longevity–income relationship," Journal of Population Economics, Springer;European Society for Population Economics, vol. 24(1), pages 191-211, January.

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