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Nonparametric estimation of an additive model with a link function

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Author Info
Joel Horowitz () (Institute for Fiscal Studies and Northwestern University)
Enno Mammen

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Abstract

This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n-2/5. This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality. Moreover, the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.

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Publisher Info
Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP19/02.

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Length: 34 pp.
Date of creation: Jul 2002
Date of revision:
Handle: RePEc:ifs:cemmap:19/02

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. J. Fan & W. H"Ardle & E. Mammen, . "Direct estimation of low dimensional components in additive models," Sonderforschungsbereich 373 1996-17, Humboldt Universitaet Berlin.
  2. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation, Yale University. [Downloadable!]
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  3. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July. [Downloadable!] (restricted)
  4. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  5. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Joel Horowitz & Sokbae 'Simon' Lee, 2004. "Nonparametric estimation of an additive quantile regression model," CeMMAP working papers CWP07/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  2. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," CeMMAP working papers CWP14/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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  3. Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a SemiparametricCharacteristic-Based Factor Model of Security Returns," STICERD - Econometrics Paper Series /2007/524, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  4. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Boston College Working Papers in Economics 585, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
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  5. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September. [Downloadable!] (restricted)
  6. Oliver Linton & Enno Mammen, 2003. "Estimating Semiparametric ARCH (8) Models by Kernel Smoothing Methods," STICERD - Econometrics Paper Series /2003/453, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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