A Result of Convergence about Weighted Sum for Exchangeable Random Variable Sequence in the Errors-in-Variables Model

A Result of Convergence about Weighted Sum for Exchangeable Random Variable Sequence in the Errors-in-Variables Model

Mei Yang 

Chongqing College of Electronic Engineering, Chongqing 401331, China

Corresponding Author Email: 
meizi11106@163.com
Page: 
322-332
|
DOI: 
https://doi.org/10.18280/ama_a.540214
Received: 
11 June 2017
|
Accepted: 
18 June 2017
|
Published: 
30 June 2017
| Citation

OPEN ACCESS

Abstract: 

This thesis discusses linear EV (errors-in-variables) regression models, that is, regression models with measurement errors. Because in practice, data are often obtained with measurement errors, EV model is more fit for application than the ordinary regression model. However, it is more complicated in the statistical inference and analysis, so research about this theory is very difficult. Due to the application of statistics, when the weight function uses real variables in EV model, we extend the consistency of the weighted sum for the independent random variable sequence and obtain a result of convergence about the weighted sum for the exchangeable random variable sequence in EV model.

Keywords: 

Errors-in-variables Model, The Weight Function Contains Real Variables, Convergence about the Weighted Sum.

1. Introduction
2. Result
3. Conclusion
  References

1. B.D. Finetti, Funzione caratteristica di unfenomeno aleatorio, 1930, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat.Nat., no. 4, pp. 86-133.

2. R.F. Patterson, R.L. Taylor, Strong laws of large numbers for triangular arrays of exchangeable random variables, 1985, Stochastic Analysis and Applications, no. 3, pp. 171-187

3. G.A.F. Seber, Linear Regression Analysis, 1987, New York, Wiley.

4. P.X. Zhao, L.G. Xue, Variable selection for semiparametric varying coefficient partially linear errors-in-variables models, 2010, Journal of Multivariate Analysis, no. 8.

5. Y. Amemiya, Instrumental variable estimator for the nonlinear errors in variables model, 1985, Journal of Econometrics, no. 28, pp. 273-289.

6. J.H. You, G.M. Chen. Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model, 2005, Journal of Multivariate Analysis, vol. 97, no. 2, pp. 324-341.

7. A. Gut, Precise asympototics for record times and the associated counting process, 2002, Stoch Proc Appl, no. 101, pp. 233-239.

8. Q.H. Wang, Dimension reduction in partly linear error-in-response models with validation data, 2003, Journal of Multivariate Analysis, no. 85, pp. 234-252

9. O. Davidov, Estimating the slope in measurement error models a different perspective, 2005, Statistics & Probability Letters, vol. 71, no. 3, pp. 215-223

10. P.K. Shukla, M.E. Orazcm, O.D. Crisaue, Validation of the measurement model concept for error structure identification, 2004, Electrochemica Acta, no. 49, pp. 2881-2889.

11. H.Hong, E.Tamer, A simple estimator for nonlinear error in variable models, 2003, Journal of Econometrics, vol. 117, pp. 1-19.

12. H.F. Chen, J.M. Yang, Strong consistent coefficient estimate for errors-in-variables models, 2005, Automatica, no. 41, pp. 1025-1033.