Model checking in partial linear regression models with berkson measurement errors

Statistica Sinica

Volumn 20, Issue 4, 2010, Pages 1551-1579

  Koul, Hira L ^a   Song, Weixing ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

Asymptotically distribution free; Consistency; Local alternatives; Marked empirical process

Indexed keywords

EID: 78349245152     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. An, H. Z. and Cheng, B. (1991). A Kolmogorov-Smirnov type statistic with application to test for nonlinearity in time series. Internat. Statist. Rev. 59, 287-307.
2. Billingsley, P. (1968). Convergence of Probability Measure. Wiley, New York.
3. Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement Error in Nonlinear Models. Chapman & Hall/CRC, Boca Raton.
4. Delaigle, A., Hall, P. and Qiu, P. H. (2006). Nonparametric methods for solving the Berkson errors-in-variables problem. J. Roy. Statist. Soc. Ser. B 68, 201-220.
5. Hart, J. D. (1997). Nonparametric Smoothing and Lack-of-Fit Tests. Springer-Verlag, New York.
6. Hu, Y. and Schennach, S. M. (2008). Instrumental variable treatment of nonclassical measurement error models. Econometrica 76, 195-216.
7. Huwang, L. and Huang, H. Y. S. (2000). On errors-in-variables in polynomial regression - Berkson case. Statist. Sinica 10, 923-936.
8. Jennrich, R. J. (1969). Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist. 40, 633-643.
9. 2 tests for testing parametric hypotheses. Theory Probab. Appl. 24, 283-301.
10. Khmaladze, E. V. and Koul, H. L. (2004). Martingale transforms goodness-of-fit tests in regression models. Ann. Statist. 32, 995-1034.
11. Koul, H. L. (2006). Model diagnostics via martingale transforms: a brief review. Frontiers in Statistics, 183-206, Imp. Coll. Press, London.
12. Koul, H. L. and Song, W. (2008). Model checking with Berkson measurement errors. J. Statist. Plann. Inference 138, 1615-1628.
13. Liang, H. (2006). Checking linearity of non-parametric component in partially linear models with an application in systemic inflammatory response syndrome study. Statist. Meth. Medical Res. 15, 273-284.
14. Lubin, J. H., Wang, Z. Y., Wang, L. D., Boice, Jr, J. D., Cui, H. X., Zhang, S. R., Conrath, S., Xia, Y., Shang, B., Cao, J. S. and Kleinerman, R. A.(2005). Adjusting lung cancer risks for temporal and spatial variations in radon concentration in dwellings in Gansu Province, China. Radn Res. 163, 571-579.
15. Raaschou-Nielsen, O., Hertel, O., Thomsen, B. and Olsen, J. (2001). Air pollution from traffic at the residence of children with cancer. Am. J. Epidem. 153, 433-443.
16. Reeves, G. K., Cox, D. R., Darby, S. C. and Whitley, E. (1998). Some aspects of measurement error in explanatory variables for continuous and binary regression models. Statist. Med. 17, 2157-2177.
17. Stram, D. O., Huberman, M. and Wu, A. H. (2002). Is residual confounding a reasonable explanation for the apparent protective effects of beta-carotene found in epidemiological studies of lung cancer in smokers? Am. J. Epidem. 155, 622-628.
18. Stute, W., Thies, S. and Zhu, L. X. (1998). Model checks for regression: an innovation process approach. Ann. Statist. 26 1916-1934. (Pubitemid 128376913)
19. Stute, W. and Zhu, L. X. (2002). Model checks for generalized linear models. Scand. J. Statist 29, 535-545.
20. Stute, W. and Zhu, L. X. (2005). Nonparametric checks for single-index models. Ann. Statist. 33, 1048-1083.
21. Thomas, D., Bowman, J., Jiang, L., Jiang, F. and Peters, J. (1999). Residential magnetic fields predicted from wiring configurations: II, Relationships to childhood leukemia. Bioelectromagnetics 20, 414-422. (Pubitemid 129549308)
22. von Neumann, J. (1941). Distribution of the ratio of the mean square successive difference to the variance. Ann. Math. Statist. 12, 367-395.
23. Wang, L. (2004). Estimation of nonlinear models with Berkson measurement errors. Ann. Statist. 32, 2559-2579.
24. Zhu, L. X. and Ng, Kai W. (2003). Checking the adequacy of a partial linear model. Satist. Sinica 13, 763-781.