Testing the adequacy for a general linear errors-in-variables model

Statistica Sinica

Volumn 15, Issue 4, 2005, Pages 1049-1068

  Zhu, Lixing ^a   Cui, Hengjian ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b NONE

Author keywords

Bias correction; Errors in variables model; Lack of fit test

Indexed keywords

EID: 30744457301     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Anderson, T. W. (1984). Estimating linear statistical relationships. Ann. Statist. 12, 1-45.
2. Behnen, K. and Neuhaus, G. (1989). Rank Tests with Estimated Scores and Their Application. B. G. Neubner Stuttgart, Germany.
3. Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement Error on Nonlinear Models. Monographs on Statistics and Applied Probability. Chapman and Hall, Now York.
4. Carroll, R. J. and Spiegelman, C. H. (1992). Diagnostics for nonlinearity and heteroscedasticity in errors-in-variables regression. Technometrics 34, 186-196.
5. Cheng, C. L. and Schneeweiss H. (1998). Polynomial regression with errors in the variables. J. R. Statist. Soc. B 60, 189-199.
6. Cheng, C. L. and Van Ness, J. W.(1999). Statistical Regression with Measurement Error. Arnold, London.
7. Cheng, C. L. and Kukush, A. (2004). A goodness-of-fit test for a polynomial errors-in-variables model. Ukrainian Math. J. 56, 527-543.
8. Cook, R. D. and Weisberg, S. (1982). Residual and Influence in Regression. Chapman and Hall, New York
9. Eubank, R. L. and Hart, J. D. (1993). Commonalty of cusum, von Neumann and smoothing-based goodness-of-fit tests. Biometrika 80, 89-98.
10. Eubank, R. L. and Spiegelman, C. H. (1990). Testing the goodness of fit of a linear model via nonparametric regression techniques. J. Amer. Statist. Assoc. 85, 387-392.
11. Fuller, W. A. (1987). Measurement Error Models. John Wiley, New York.
12. Hall, P. and Hart, J. D. (1990). Bootstrap test for difference between means in nonparametric regression. J. Amer. Statist. Assoc. 85, 1039-1049.
13. Härdle, W. and Mammen, E. (1993). Comparing non-parametric versus parametric regression fits. Ann. Statist. 21, 1926-1947.
14. Härdle, W., Mammen, E. and Müller, M. (1998). Testing parametric versus semiparametric modeling in generalized linear models. J. Amer. Statist. Assoc. 93, 1461-1474.
15. Hart, J. D. (1997). Nonparametric Smoothing and Lack-of-Fit Tests. Springer Series in Statistics, New York.
16. He, X. and Ng, P. (1999). Quantile splines with several covariates. J. Statist. Plann. Inference 75, 343-352.
17. Stefanski, L. A. and Carroll, R. J. (1991). Deconvolution-based score tests in measurement error models. Ann. Statist. 19, 249-259.
18. Sepanski, J. H. and Lee, L. F. (1995). Semiparametric estimation of nonlinear error-in-variables models with validation study. J. Nonparametr. Statist. 4, 365-394.
19. Strasser, H. (1985). Mathematical Theory of Statistics. De Gruyter, Berlin.
20. Stute, W. (1997). Nonparametric model checks for regression. Ann. Statist. 25, 613-641.
21. Stute, W., Gonzalez Manteiga, G. and Quindimil, M. P. (1998). Bootstrap approximations in model checks for regression. J. Amer. Statist. Asso. 93, 141-149.
22. Stute, W., Thies, S. and Zhu, L. X. (1998). Model checks for regression: An innovation process approach. Ann. Statist. 26, 1916-1934.
23. Stute, W. and Zhu, L. X.(2002). Model checks for generalized linear models. Scan. J. Statist. 29, 535-546.
24. Stute, W. and Zhu, L. X.(2005). Nonparametric checks for single-index models. Ann. Statist. 33, 1048-1085.
25. Zhu, L. X. (2003). Model checking of dimension-reduction type for regression. Statist. Sinica 13, 283-296.
26. Zhu, L. X., Cui, H. J. and Ng, K. W. (2004). Testing lack-of-test for linear errors-in-variables model. Acta Math. Appl. Sinica 20, 533-540.
27. Zhu, L. X. and Ng, K. W. (2003). Checking the adequacy of a partial linear model. Statist. Sinica 13, 763-781.
28. Zhu, L. X., Song, W. X. and Cui, H. J. (2004). Testing lack-of-fit for a polynomial errors-in-variables model, Acta, Math. Appl. Sinica 19, 353-362.