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ON CONSISTENCY OF LS ESTIMATORS IN THE ERRORS-IN-VARIABLE REGRESSION MODEL

Published online by Cambridge University Press:  01 December 2016

Xuejun Wang ,
Mengmei Xi ,
Hongxia Wang  and
Shuhe Hu
Xuejun Wang
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: [email protected]
Mengmei Xi
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China E-mail: [email protected]
Hongxia Wang
Affiliation:
Department of Statistics, Nanjing Audit University, Nanjing 211815, People's Republic of China
Shuhe Hu
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, People's Republic of China
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Abstract

Under some mild conditions, the strong consistency and complete consistency of the LS estimators in the errors-in-variable regression model with weakly negative dependent errors are obtained, which generalize the corresponding ones for negatively associated random variables. In addition, the simulation study shows that the biases of our method are small, and our method performs well.

Keywords

complete consistencyEV regression modelstrong consistencyweakly negative dependent random variables
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 1 , January 2018 , pp. 144 - 162
Copyright
Copyright © Cambridge University Press 2016 

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References

1. Amemiya, Y. & Fuller, W.A. (1984). Estimation for the multivariate errors-in-variables model with estimated error covariance matrix. The Annals of Statistics 12: 497–509.CrossRefGoogle Scholar
2. Carroll, R.J., Ruppert, D., Crainiceanu, C., Tosteson, T.D., & Karagas, M.R. (2004). Nonlinear and nonparametric regression and instrumental Variables. Journal of the American Statistical Association 99: 736–750.Google Scholar
3. Chen, Y., Chen, A., & Ng, K.W. (2010). The strong law of large numbers for extend negatively dependent random variables. Journal of Applied Probability 47: 908–922.CrossRefGoogle Scholar
4. Cui, H.J. & Chen, S.X. (2003). Empirical likelihood confidence region for parameter in the errors-in-variables models. Journal of Multivariate Analysis 84: 101–115.Google Scholar
5. Dagenais, M.G. & Dagenais, D.L. (1997). Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics 76: 193–221.Google Scholar
6. Deaton, A. (1985). Panel data from a time series of cross-sections. Journal of Econometrics 30: 109–126.Google Scholar
7. Fan, G.L., Liang, H.Y., Wang, J.F., & Xu, H.X. (2010). Asymptotic properties for LS estimators in EV regression model with dependent errors. AStA-Advances in Statistical Analysis 94: 89–103.CrossRefGoogle Scholar
8. Gleser, L.J. (1981). Estimation in a multivariate ‘errors in variables’ regression model: large sample results. The Annals of Statistics 9: 24–44.Google Scholar
9. Hslao, C., Wang, L., & Wang, Q. (1997). Estimation of nonlinear errors-in-variables models: an approximate solution. Statistical Papers 38: 1–25.Google Scholar
10. Jing, B.Y. & Liang, H.Y. (2008). Strong limit theorems for weighted sums of negatively associated random variables. Journal of Theoretical Probability 21: 890–909.Google Scholar
11. Jung, K.-M. (2007). Least trimmed squares estimator in the errors-in-variables model. Journal of Applied Statistics 34: 331–338.CrossRefGoogle Scholar
12. Lai, T.L., Robbins, H., & Wei, C.Z. (1979). Strong consistency of least squares estimates in multiple regression. Journal of Multivariate Analysis 9: 343–362.Google Scholar
13. Li, T. (2002). Robust and consistent estimation of nonlinear errors-in-variables models. Journal of Econometrics 110: 1–26.Google Scholar
14. Liu, J.X. & Chen, X.R. (2005). Consistency of LS estimator in simple linear EV regression models. Acta Mathematica Scientia B 25: 50–58.CrossRefGoogle Scholar
15. Liu, L. (2009). Precise large deviations for dependent random variables with heavy tails. Statistics and Probability Letters 79: 1290–1298.Google Scholar
16. Miao, Y., Wang, Y.L. & Zheng, H.J. (2015). Consistency of LS estimators in the EV regression model with martingale difference errors. Statistics: A Journal of Theoretical and Applied Statistics 49: 104–118.Google Scholar
17. Miao, Y., Zhao, F.F., Wang, K., & Chen, Y.P. (2013). Asymptotic normality and strong consistency of LS estimators in the EV regression model with NA errors. Statistical Papers 54: 193–206.Google Scholar
18. Qiu, D.H., Chen, P.Y., Antonini, R.G., & Volodin, A. (2013). On the complete convergence for arrays of rowwise extended negatively dependent random variables. Journal of the Korean Mathematical Society 50: 379–392.Google Scholar
19. Ranjbar, V., Amini, M., & Bozorgnia, A. (2009). Asympotic behavior of convolution of dependent random variables with heavy-tail distribution. Thai Journal of Mathematics 7: 21–34.Google Scholar
20. Ranjbar, V., Amini, M., Geluk, J., & Bozorgnia, A. (2013). Asympotic behavior of product of two heavy-tail dependent random variables. Acta Mathematica Sinica, English Series 29: 355–364.Google Scholar
21. Shen, A.T. (2011). Probability inequalities for END sequence and their applications. Journal of Inequalities and Applications 2011: 12 pages, Article ID 98.CrossRefGoogle Scholar
22. Shen, A.T. (2013). On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables. RACSAM 107: 257–271.CrossRefGoogle Scholar
23. Shen, A.T. (2014). On asymptotic approximation of inverse moments for a class of nonnegative random variables. Statistics: A Journal of Theoretical and Applied Statistics 48: 1371–1379.Google Scholar
24. Shen, A.T., Zhang, Y., & Volodin, A. (2015). Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables. Metrika 78: 295–311.CrossRefGoogle Scholar
25. Stout, W.F. (1974). Almost sure convergence. New York: Academic Press.Google Scholar
26. Taupin, M.L. (2001). Semiparametric estimation in the nonlinear structural errors-in-variables model. The Annals of Statistics 29: 66–93.Google Scholar
27. Wang, S.J. & Wang, X.J. (2013). Precise large deviations for random sums of END real-valued random variables with consistent variation. Journal of Mathematical Analysis and Applications 402: 660–667.Google Scholar
28. Wang, X.J., Li, X.Q., Hu, S.H., & Wang, X.H. (2014). On complete convergence for an extended negatively dependent sequence. Communications in Statistics – Theory and Methods 43: 2923–2937.Google Scholar
29. Wang, X.J., Shen, A.T., Chen, Z.Y., & Hu, S.H. (2015). Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. TEST 24: 166–184.Google Scholar
30. Wang, X.J., Wang, S.J., Hu, S.H., Ling, J.M., & Wei, Y.F. (2013). On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables. Stochastics: An International Journal of Probability and Stochastic Processes 85: 1060–1072.Google Scholar
31. Wang, X.J., Zheng, L.L., Xu, C., & Hu, S.H. (2015). Complete consistency for the estimator of nonparametric regression models based on extended negatively dependent errors. Statistics: A Journal of Theoretical and Applied Statistics 49: 396–407.Google Scholar
32. Wu, Y.F. & Guan, M. (2012). Convergence properties of the partial sums for sequences of END random variables. Journal of the Korean Mathematical Society 49: 1097–1110.Google Scholar