Multivariate partially linear regression in the presence of measurement error

Original Paper
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Abstract

In this paper, multivariate partially linear model with error in the explanatory variable of nonparametric part, where the response variable is m dimensional, is considered. By modification of local-likelihood method, an estimator of parametric part is driven. Moreover, the asymptotic normality of the generalized least square estimator of the parametric component is investigated when the error distribution function is either ordinarily smooth or super smooth. Applications in the Engel curves are discussed and through Monte Carlo experiments performances of \(\hat{\beta }_{n}\) are investigated.

Keywords

Multivariate regression Partially linear models Errors in variables Kernel smoothing Asymptotic normality 

References

  1. Blundell, R., Duncan, A., Pendakur, K.: Semiparametric estimation of consumer demand. J. Appl. Econom. 13, 435–461 (1998).  https://doi.org/10.1002/(SICI)1099-1255(1998090)13:5%3c435::AID-JAE506%3e3.0.CO;2-K CrossRefGoogle Scholar
  2. Fan, J., Masry, E.: Multivariate regression estimation with errors-in-variables: asymptotic normality for mixing processes. J. Multivar. Anal. 43, 237–271 (1992).  https://doi.org/10.1016/0047-259X(92)90036-F MathSciNetCrossRefMATHGoogle Scholar
  3. Fan, J., Truong, Y.K.: Nonparametric regression with errors in variables. Ann. Stat. 21, 1900–1925 (1993)MathSciNetCrossRefMATHGoogle Scholar
  4. Fuller, W.A.: Measurement Error Models. Wiley, New York (1987)CrossRefMATHGoogle Scholar
  5. Liang, H.: Asymptotic normality of parametric part in partially linear model with measurement error in the non-parametric part. J. Stat. Plann. Inference 86, 51–62 (2000).  https://doi.org/10.1016/S0378-3758(99)00093-2 CrossRefMATHGoogle Scholar
  6. Lopez, B.P., Manteiga, W.G.: Multivariate partially linear model. Stat. Probab. Lett. 76, 1543–1549 (2006).  https://doi.org/10.1016/j.spl.2006.03.016 MathSciNetCrossRefMATHGoogle Scholar
  7. Masry, E.: Multivariate probability density deconvolution for stationary random processes. IEEE Trans. Inform. Theory 37, 1105–1115 (1991).  https://doi.org/10.1109/18.87002 MathSciNetCrossRefMATHGoogle Scholar
  8. Masry, E.: Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes. J. Multivar. Anal. 44, 47–68 (1993a).  https://doi.org/10.1006/jmva.1993.1003 MathSciNetCrossRefMATHGoogle Scholar
  9. Masry, E.: Strong consistency and rates for deconvolution of multivariate densities of stationary processes. Stoch. Process. Appl. 47, 53–74 (1993b).  https://doi.org/10.1016/0304-4149(93)90094-K MathSciNetCrossRefMATHGoogle Scholar
  10. Masry, E.: Multivariate regression estimation with errors in variables for stationary processes. Nonparametr. Statist. 3, 13–36 (1993c).  https://doi.org/10.1080/10485259308832569 MathSciNetCrossRefMATHGoogle Scholar
  11. Phlips, L.: Applied Consumption Analysis. North-Holland, Amsterdam (1974)Google Scholar
  12. Robinson, P.: Root-N-consistent semiparametric regression. Econometrica 56, 931–954 (1988).  https://doi.org/10.2307/1912705 MathSciNetCrossRefMATHGoogle Scholar
  13. Toprak, S.: Semiparametric regression models with errors in variables. PhD Thesis. Dicle University, Diyarbakir (2015). https://tez.yok.gov.tr/UlusalTezMerkezi/tezSorguSonucYeni.jsp

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceDicle UniversitySurTurkey

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