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On The Uniform Convergence Of Deconvolution Estimators From Repeated Measurements

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  • Kurisu, Daisuke
  • Otsu, Taisuke

Abstract

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

Suggested Citation

  • Kurisu, Daisuke & Otsu, Taisuke, 2022. "On The Uniform Convergence Of Deconvolution Estimators From Repeated Measurements," Econometric Theory, Cambridge University Press, vol. 38(1), pages 172-193, February.
    • Handle: RePEc:cup:etheor:v:38:y:2022:i:1:p:172-193_5
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    Cited by:

    1. Hao Dong & Yuya Sasaki, 2022. "Estimation of average derivatives of latent regressors: with an application to inference on buffer-stock saving," Departmental Working Papers 2204, Southern Methodist University, Department of Economics.

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