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Convolution without independence

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  • Susanne Schennach

    (Institute for Fiscal Studies and Brown University)

Abstract

Widely used convolutions and deconvolutions techniques traditionally rely on the assumption of independence, an assumption often criticised as being very strong. We observe that independence is, in fact, not necessary for the convolution theorem to hold. Instead, a much weaker notion, known as subindependence, is the appropriate necessary and sufficient condition. We motivate the usefulness of the subindependence concept by showing that it is arguably as week as a conditional mean assumption. We also provide and devise a constructive method to generate pairs of subindependent random variables.

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File URL: http://www.cemmap.ac.uk/wps/cwp461313.pdf
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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP46/13.

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Date of creation: Sep 2013
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Handle: RePEc:ifs:cemmap:46/13

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  1. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
  2. Stéphane Bonhomme & Jean-Marc Robin, 2008. "Generalized nonparametric deconvolution with an application to earnings dynamics," CeMMAP working papers CWP03/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, 04.
  4. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, 01.
  5. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  6. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(03), pages 546-581, June.
  7. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
  8. Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
  9. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  10. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  11. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
  12. Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
  13. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
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