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Nonparametric Estimation with Aggregated Data

  • Oliver Linton
  • Yoon-Jae Whang

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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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
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. 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.
  2. Enno Mammen & Oliver Linton & J Nielsen, 2000. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 2315, London School of Economics and Political Science, LSE Library.
  3. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, EconWPA.
  4. repec:cup:etheor:v:13:y:1997:i:2:p:170-84 is not listed on IDEAS
  5. Oliver Linton & E. Mammen & J. Nielsen & C. Tanggaard, 1998. "Estimating Yield Curves by Kernel Smoothing Methods," Cowles Foundation Discussion Papers 1205, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Knight, John L. & Satchell, Stephen E., 1997. "The Cumulant Generating Function Estimation Method," Econometric Theory, Cambridge University Press, vol. 13(02), pages 170-184, April.
  8. Donald W.K. Andrews & Yoon-Jae Whang, 1989. "Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality," Cowles Foundation Discussion Papers 925, Cowles Foundation for Research in Economics, Yale University.
  9. repec:cup:etheor:v:6:y:1990:i:4:p:466-79 is not listed on IDEAS
  10. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  11. Horowitz, Joel L & Markatou, Marianthi, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 145-68, January.
  12. 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.
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