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Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes

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  • Fan, Jianqing
  • Masry, Elias

Abstract

Errors-in-variables regression is the study of the association between covariates and responses where covariates are observed with errors. In this paper, we consider the estimation of multivariate regression functions for dependent data with errors in covariates. Nonparametric deconvolution technique is used to account for errors-in-variables. The asymptotic behavior of regression estimators depends on the smoothness of the error distributions, which are characterized as either ordinarily smooth or super smooth. Asymptotic normality is established for both strongly mixing and [varrho]-mixing processes, when the error distribution function is either ordinarily smooth or super smooth.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 43 (1992)
Issue (Month): 2 (November)
Pages: 237-271

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Handle: RePEc:eee:jmvana:v:43:y:1992:i:2:p:237-271

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Related research

Keywords: asymptotic normality deconvolution errors-in-variables multivariate regression mixing processes;

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Cited by:
  1. Oliver Linton & Yoon-Jae Whang, 2000. "Nonparametric Estimation with Aggregated Data," STICERD - Econometrics Paper Series /2000/397, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.
  3. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
  4. Masry, Elias & Mielniczuk, Jan, 1999. "Local linear regression estimation for time series with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 173-193, August.
  5. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
  6. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Inference for Integrated Volatility," Departmental Working Papers 200616, Rutgers University, Department of Economics.
  7. Ioannides, D. A. & Alevizos, P. D., 1997. "Nonparametric regression with errors in variables and applications," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 35-43, February.
  8. Delaigle, Aurore & Meister, Alexander, 2007. "Nonparametric Regression Estimation in the Heteroscedastic Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1416-1426, December.
  9. Comte, F. & Lacour, C. & Rozenholc, Y., 2010. "Adaptive estimation of the dynamics of a discrete time stochastic volatility model," Journal of Econometrics, Elsevier, vol. 154(1), pages 59-73, January.
  10. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
  11. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.

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