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ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

Published online by Cambridge University Press:  25 January 2021

Daisuke Kurisu  and
Taisuke Otsu
Daisuke Kurisu
Affiliation:
Tokyo Institute of Technology
Taisuke Otsu*
Affiliation:
London School of Economics
*
Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, LondonWC2A 2AE, UK; e-mail: [email protected].
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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.

Type
MISCELLANEA
Information
Econometric Theory , Volume 38 , Issue 1 , February 2022 , pp. 172 - 193
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

The authors would like to thank anonymous referees for helpful comments. Our research is supported by JSPS KAKENHI (JP17H02513, JP19K20881, and JP20K13468; Kurisu) and ERC Consolidator Grant (SNP 615882; Otsu).

References

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