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Nonparametric Estimation With Aggregated Data

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  • Linton, Oliver
  • Whang, Yoon-Jae

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 intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

Suggested Citation

  • Linton, Oliver & Whang, Yoon-Jae, 2002. "Nonparametric Estimation With Aggregated Data," Econometric Theory, Cambridge University Press, vol. 18(2), pages 420-468, April.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:02:p:420-468_18
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    Cited by:

    1. Marie-Hélène Felt, 2018. "A Look Inside the Box: Combining Aggregate and Marginal Distributions to Identify Joint Distributions," Staff Working Papers 18-29, Bank of Canada.
    2. Meister, Alexander, 2007. "Optimal convergence rates for density estimation from grouped data," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1091-1097, June.
    3. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
    4. Joel L. Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers CWP37/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Raymond J. Carroll & Aurore Delaigle & Peter Hall, 2007. "Non‐parametric regression estimation from data contaminated by a mixture of Berkson and classical errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 859-878, November.
    6. Carroll, Raymond J. & Delaigle, Aurore & Hall, Peter, 2009. "Nonparametric Prediction in Measurement Error Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 993-1003.
    7. Phuong, Cao Xuan & Thuy, Le Thi Hong, 2019. "Density deconvolution from grouped data with additive errors," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 74-81.
    8. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
    9. 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 for Research in Economics, Yale University.
    10. Joel L. Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers 37/13, Institute for Fiscal Studies.
    11. Felt, Marie-Hélène, 2020. "On the identification of joint distributions using marginals and aggregates," Economics Letters, Elsevier, vol. 194(C).

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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