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Convolution without independence

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  • Schennach, Susanne M.

Abstract

Widely used convolution and deconvolution techniques traditionally rely on independence assumptions, often criticized as being strong. We observe that the convolution theorem actually holds under a weaker assumption, known as subindependence. We show that this notion is arguably as weak as a conditional mean assumption. We report various simple characterizations of subindependence and devise constructive methods to generate subindependent random variables. We extend subindependence to multivariate settings and propose the new concepts of conditional and mean subindependence, relevant to measurement error problems. We finally introduce three tests of subindependence based on characteristic functions, generalized method of moments and randomization, respectively.

Suggested Citation

  • Schennach, Susanne M., 2019. "Convolution without independence," Journal of Econometrics, Elsevier, vol. 211(1), pages 308-318.
  • Handle: RePEc:eee:econom:v:211:y:2019:i:1:p:308-318
    DOI: 10.1016/j.jeconom.2018.12.018
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    4. Stéphane Bonhomme & Jean-Marc Robin, 2010. "Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 491-533.
    5. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers CWP41/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Daniel Wilhelm, 2015. "Identification and estimation of nonparametric panel data regressions with measurement error," CeMMAP working papers CWP34/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. 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, April.
    8. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    9. Yingyao Hu & Geert Ridder, 2010. "On Deconvolution as a First Stage Nonparametric Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 29(4), pages 365-396.
    10. Susanne M. Schennach, 2016. "Recent Advances in the Measurement Error Literature," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 341-377, October.
    11. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843 Elsevier.
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    Cited by:

    1. repec:cup:etheor:v:34:y:2018:i:01:p:134-165_00 is not listed on IDEAS
    2. Karun Adusumilli & Taisuke Otsu & Yoon-Jae Whang, 2017. "Inference on distribution functions under measurement error," STICERD - Econometrics Paper Series 594, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. repec:eee:econom:v:200:y:2017:i:2:p:312-325 is not listed on IDEAS
    4. repec:eee:econom:v:207:y:2018:i:1:p:129-161 is not listed on IDEAS

    More about this item

    Keywords

    Subindependence; Measurement error; Error-in-variables; Deconvolution; Characteristic function;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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