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Measurement Error And Deconvolution In Spaces Of Generalized Functions

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  • Zinde-Walsh, Victoria

Abstract

This paper considers convolution equations that arise from problems such as measurement error and nonparametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions to account for possible singularities; this makes it possible to consider densities for arbitrary and not only absolutely continuous distributions, and to operate with Fourier transforms for polynomially growing regression functions. Results are derived for identification and well-posedness in the topology of generalized functions for the deconvolution problem and for some regression models. Conditions for consistency of plug-in estimation for these models are provided.

Suggested Citation

  • Zinde-Walsh, Victoria, 2014. "Measurement Error And Deconvolution In Spaces Of Generalized Functions," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1207-1246, December.
    • Handle: RePEc:cup:etheor:v:30:y:2014:i:06:p:1207-1246_00
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    Cited by:

    1. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(4), pages 925-932, August.
    2. De Nadai, Michele & Lewbel, Arthur, 2016. "Nonparametric errors in variables models with measurement errors on both sides of the equation," Journal of Econometrics, Elsevier, vol. 191(1), pages 19-32.
    3. Janderson R. Rodrigues & Utsav D. Dave & Aseema Mohanty & Xingchen Ji & Ipshita Datta & Shriddha Chaitanya & Euijae Shim & Ricardo Gutierrez-Jauregui & Vilson R. Almeida & Ana Asenjo-Garcia & Michal L, 2023. "All-dielectric scale invariant waveguide," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    4. Ben-Moshe, Dan & D’Haultfœuille, Xavier & Lewbel, Arthur, 2017. "Identification of additive and polynomial models of mismeasured regressors without instruments," Journal of Econometrics, Elsevier, vol. 200(2), pages 207-222.
    5. Oliver Linton & Ji-Liang Shiu, 2018. "Semiparametric nonlinear panel data models with measurement error," CeMMAP working papers CWP09/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    7. Ben-Moshe, Dan, 2018. "Identification Of Joint Distributions In Dependent Factor Models," Econometric Theory, Cambridge University Press, vol. 34(1), pages 134-165, February.

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