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Nonparametric Estimation with Aggregated Data

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Author Info
Oliver Linton
Yoon-Jae Whang

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Abstract

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intra-family component but require that observations from different families be in dependent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behaviour of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment

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Publisher Info
Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/397.

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Date of creation: Jul 2000
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Handle: RePEc:cep:stiecm:/2000/397

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Keywords: Aggregated data; deconvolution; grouped data; kernel; nonparametric regression;

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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. Oliver Linton & E. Mammen & J. Nielsen & C. Tanggaard, 1998. "Estimating Yield Curves by Kernel Smoothing Methods," Cowles Foundation Discussion Papers 1205, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, EconWPA. [Downloadable!]
  3. Andrews, Donald W.K. & Whang, Yoon-Jae, 1990. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Econometric Theory, Cambridge University Press, vol. 6(04), pages 466-479, December. [Downloadable!]
    Other versions:
  4. Masry, E., 1993. "Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 47-68, January. [Downloadable!] (restricted)
  5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  6. repec:cup:etheor:v:6:y:1990:i:4:p:466-79 is not listed on IDEAS
  7. repec:cup:etheor:v:13:y:1997:i:2:p:170-84 is not listed on IDEAS
  8. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November. [Downloadable!] (restricted)
  9. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  10. Horowitz, Joel L & Markatou, Marianthi, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Blackwell Publishing, vol. 63(1), pages 145-68, January. [Downloadable!] (restricted)
  11. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
  12. Andrew Chesher, 1997. "Diet Revealed?: Semiparametric Estimation of Nutrient Intake-Age Relationships," Journal Of The Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 389-428. [Downloadable!] (restricted)
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Cited by:
(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. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation, Yale University. [Downloadable!]
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