Communications for Statistical Applications and Methods

  • 제27권5호
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  • Pages.511-521
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  • 2020
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Partially linear multivariate regression in the presence of measurement error

  • Yalaz, Secil (Department of Statistics, Dicle University) ;
  • Tez, Mujgan (Department of Statistics, Marmara University)
  • 투고 : 2020.03.01
  • 심사 : 2020.06.02
  • 발행 : 2020.09.30
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초록

In this paper, a partially linear multivariate model with error in the explanatory variable of the nonparametric part, and an m dimensional response variable is considered. Using the uniform consistency results found for the estimator of the nonparametric part, we derive an estimator of the parametric part. The dependence of the convergence rates on the errors distributions is examined and demonstrated that proposed estimator is asymptotically normal. In main results, both ordinary and super smooth error distributions are considered. Moreover, the derived estimators are applied to the economic behaviors of consumers. Our method handles contaminated data is founded more effectively than the semiparametric method ignores measurement errors.

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참고문헌

  1. Blundell R, Duncan A, and Pendakur K (1998). Semiparametric estimation of consumer demand, Journal of Applied Econometrics, 13, 435-461. https://doi.org/10.1002/(SICI)1099-1255(1998090)13:5<435::AID-JAE506>3.0.CO;2-K
  2. Fan J and Masry E (1992). Multivariate regression estimation with errors-in-variables: asymptotic normality for mixing processes, Journal of Multivariate Analysis, 43, 237-271. https://doi.org/10.1016/0047-259X(92)90036-F
  3. Fan J and Truong YK (1993). Nonparametric regression with errors in variables, The Annals of Statistics, 21, 1900-1925. https://doi.org/10.1214/aos/1176349402
  4. Fuller WA (1987). Measurement Error Models, John Wiley & Sons, New York.
  5. Ioannides DA and Alevizos PD (1997). Nonparametric regression with errors in variables and applications, Statistics and Probability Letters, 32, 35-43. https://doi.org/10.1016/S0167-7152(96)00054-5
  6. Liang H (2000). Asymptotic normality of parametric part in partially linear model with measurement error in the non-parametric part, Journal of Statistical Planning and Inference, 86, 51-62. https://doi.org/10.1016/S0378-3758(99)00093-2
  7. Liang H, Hardle W, and Carroll RJ (1999). Estimation in a Semiparametric partially linear errors in variables model, The Annals of Statistics, 27, 1519-1535. https://doi.org/10.1214/aos/1017939140
  8. Masry E (1991). Multivariate probability density deconvolution for stationary random processes, IEEE Transactions on Information Theory, 37, 1105-1115. https://doi.org/10.1109/18.87002
  9. Masry E (1993a). Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes, Journal of Multivariate Analysis, 44, 47-68. https://doi.org/10.1006/jmva.1993.1003
  10. Masry E (1993b). Strong consistency and rates for deconvolution of multivariate densities of stationary processes, Stochastic Processes and their Applications, 47, 53-74. https://doi.org/10.1016/0304-4149(93)90094-K
  11. Masry E (1993c). Multivariate regression estimation with errors in variables for stationary processes, Journal of Nonparametric Statistics, 3, 13-36. https://doi.org/10.1080/10485259308832569
  12. Robinson PM (1988). Root-N-Consistent semiparametric regression, Econometrica, 56, 931-954. https://doi.org/10.2307/1912705
  13. Stefanski L and Carroll RJ (1990). Deconvoluting kernel density estimators, Statistics, 21, 164-184.
  14. Toprak S (2015). Semiparametric regression models with errors in variables, (Doctoral dissertation), Dicle University, Turkey.
  15. Yalaz S (2019). Multivariate partially linear regression in the presence of measurement error, AStA Advances in Statistical Analysis, 103, 123-135. https://doi.org/10.1007/s10182-018-0326-7
  16. Zhu L and Cui H (2003). A semi-parametric regression model with errors in variables, Scandinavian Journal of Statistics, 30, 429-442. https://doi.org/10.1111/1467-9469.00340