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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

REFERENCES

Adusumilli, K., Kurisu, D., Otsu, T., & Whang, Y.J. (2020) Inference on distribution functions under measurement error. Journal of Econometrics 215, 131–164.CrossRefGoogle Scholar
Adusumilli, K. & Otsu, T. (2018) Nonparametric instrumental regression with errors in variables. Econometric Theory 34, 1256–1280.CrossRefGoogle Scholar
Arcidiacono, P., Aucejo, E.M., Fang, H., & Spenner, K.I. (2011) Does affirmative action lead to mismatch? A new test and evidence. Quantitative Economics 2, 303–333.CrossRefGoogle Scholar
Arellano, M. & Bonhomme, S. (2012) Identifying distributional characteristics in random coefficients panel data models. Review of Economic Studies 79, 987–1020.CrossRefGoogle Scholar
Athey, S. & Haile, P.A. (2007) Nonparametric approaches to auctions. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics, vol. 6A, pp. 3847–3965. Elsevier.CrossRefGoogle Scholar
Bonhomme, S. & Robin, J.-M. (2010) Generalized non-parametric deconvolution with an application to earnings dynamics. Review of Economic Studies 77, 491–533.CrossRefGoogle Scholar
Comte, F. & Kappus, J. (2015) Density deconvolution from repeated measurement without symmetry assumption on the errors. Journal of Multivariate Analysis 140, 31–46.CrossRefGoogle Scholar
Delaigle, A., Hall, P., & Meister, A. (2008) On deconvolution with repeated measurements. Annals of Statistics 36, 665–685.CrossRefGoogle Scholar
Evdokimov, K. (2010) Identification and estimation of a nonparametric panel data model with unobserved heterogeneity, Working paper, Princeton University.Google Scholar
Evdokimov, K. & White, H. (2012) Some extensions of a lemma of Kotlarski. Econometric Theory 2012(28), 925–932.CrossRefGoogle Scholar
Fan, J. (1991) On the optimal rates of convergence for non-parametric deconvolution problems. Annals of Statistics 19, 1257–1272.CrossRefGoogle Scholar
Hall, P. & Meister, A. (2007) A ridge-parameter approach to deconvolution. Annals of Statistics 35, 1535–1558.CrossRefGoogle Scholar
Hu, Y. (2017) The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics. Journal of Econometrics 200, 154–168.CrossRefGoogle Scholar
Kato, K. & Kurisu, D. (2020) Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations. Stochastic Processes and Their Applications 130, 1159–1205.CrossRefGoogle Scholar
Kotlarski, I. (1967) On characterizing the gamma and the normal distribution. Pacific Journal of Mathematics 20, 69–76.CrossRefGoogle Scholar
Krasnokutskaya, E. (2011) Identification and estimation of auction models with unobserved heterogeneity. Review of Economic Studies 78, 293–327.CrossRefGoogle Scholar
Kurisu, D. (2019) Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein–Uhlenbeck processes under macroscopic discrete observations. Electronic Journal of Statistics 13, 2521–2565.CrossRefGoogle Scholar
Li, T. (2002) Robust and consistent estimation of nonlinear errors-in-variables models. Journal of Econometrics 110, 1–26.CrossRefGoogle Scholar
Li, T. & Hsiao, C. (2004) Robust estimation of generalized linear models with measurement errors. Journal of Econometrics 118, 51–65.CrossRefGoogle Scholar
Li, T. & Vuong, Q. (1998) Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis 65, 139–165.CrossRefGoogle Scholar
Neumann, M. & Reiss, M. (2009) Nonparametric estimation for Lévy processes from low-frequency observations. Bernoulli 15, 223–248.CrossRefGoogle Scholar
Otsu, T. & Taylor, L.N. (2019) Specification testing for errors-in-variables models. Econometric Theory, first published online on 19 June 2020. DOI:10.1017/S0266466620000262. CrossRefGoogle Scholar
Tsybakov, A.B. (2009) Introduction to Nonparametric Estimation. Springer.CrossRefGoogle Scholar
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar