Order-restricted semiparametric inference for the power bias model

Biometrics

Volumn 66, Issue 2, 2010, Pages 549-557

  Davidov, Ori ^a   Fokianos, Konstantinos ^b   Iliopoulos, George ^c  

^a UNIVERSITY OF HAIFA   (Israel)

^b UNIVERSITY OF CYPRUS   (Cyprus)

^c UNIVERSITY OF PIRAEUS   (Greece)

Author keywords

Biased sampling; Empirical likelihood; Likelihood ratio order; Pool adjacent violators algorithm (PAVA); Semiparametric models; Usual stochastic order

Indexed keywords

INFERENCE ENGINES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

BIAS MODELING; BIASED SAMPLING; EMPIRICAL LIKELIHOOD; LIKELIHOOD RATIO ORDER; POOL ADJACENT VIOLATOR ALGORITHM; POWER; SEMI-PARAMETRIC MODELING; SEMIPARAMETRIC INFERENCE; STOCHASTIC ORDERINGS; USUAL STOCHASTIC ORDER;

PROBABILITY DENSITY FUNCTION;

ALGORITHM; EMPIRICAL ANALYSIS; POPULATION DENSITY; POPULATION MODELING; PROBABILITY; SAMPLING BIAS; STOCHASTICITY;

PROBABILITY; SELECTION BIAS; STATISTICAL MODEL;

LIKELIHOOD FUNCTIONS; MODELS, STATISTICAL; PROBABILITY; SELECTION BIAS;

EID: 77953014984     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2009.01285.x     Document Type: Article

References (32)

1. Akman, O., Gamage, J., Jannot, J., Juliano, S., Thurman, A., and Whitman, D. (2007). A simple test for detection of length-biased sampling. JP Journal of Biostatistics 1, 189 195.
2. Bickel, P. J., Klaassen, C. A. J., Ritov, Y., and Wellner, J. A. (1998). Efficient and Adaptive Estimation for Semiparametric Models. Reprint of the 1993 original.
3. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization.
4. Davidov, O. and Herman, A. (2009). Testing for order among K populations: Theory and examples submitted)
5. Davidov, O. and Iliopoulos, G. (2008). On the existence and uniqueness of the NPMLE in biased sampling models. Journal of Statistical Planning and Inference 139, 176 183.
6. Davidov, O. and Iliopoulos, G. (2009). A note on an iterative algorithm for nonparametric estimation in biased sampling models. Computational Statistics and Data Analysis.
7. Davidov, O. and Zelen, M. (2001). Referent sampling, family history and relative risk: The role of length biased sampling. Biostatistics 2, 173 181.
8. El Barmi, H. (1996). Empirical likelihood ratio test for or against a set of inequality constraints. Journal of Statistical Planning and Inference 55, 191 204.
9. Fokianos, K. (2004). Merging information for semi-parametric density estimation. Journal of the Royal Statistical Society, Series B 66, 941 958.
10. Fokianos, K. (2008). Comparing two samples by penalized logistic regression. Electronic Journal of Statistics 2, 564 580.
11. Fokianos, K. and Troendle, J. F. (2007). Inference for the relative treatment effect with the density ratio moodel. Statistical Modelling 7, 155 173.
12. Fokianos, K., Kedem, B., Qin, J., and Short, D. A. (2001). A semiparametric approach to the one-way layout. Technometrics 66, 56 65.
13. Gilbert, P. B. (2000). Large sample theory of maximum likelihood estimates in semiparametric biased sampling models. The Annals of Statistics 28, 151 194.
14. Gilbert, P. B., Lele, S. R., and Vardi, Y. (1999). Maximum likelihood estimation in semiparametric selection bias models with application to AIDS vaccine trials. Biometrika 86, 27 43.
15. Gill, R. D., Vardi, Y., and Wellner, J. A. (1988). Large sample theory of empirical distributions in biased sampling models. The Annals of Statistics 16, 1069 1112.
16. Navarro, J., Ruiz, J. M., and del Aguila, Y. (2001). Parametric estimation from weighted samples. Biometrical Journal 43, 297 311. (Pubitemid 33580707)
17. Navarro, J., Ruiz, J. M., and del Aguila, Y. (2003). How to detect biased samples? Biometrical Journal 45, 91 112.
18. Owen, A. B. (2001). Empirical Likelihood.
19. Piegorsch, W. W. (1990). One-sided significance tests for generalized linear models under dichotomous response. Biometrics 46, 309 316.
20. Qin, J. (1998). Inferences for case-control and semiparametric two-sample density ratio models. Biometrika 85, 619 630.
21. Qin, J. and Zhang, B. (1997). A goodness of fit for logistic regression models based on case-control data. Biometrika 84, 609 618.
22. Robertson, T., Wright, F. T., and Dykstra, R. L. (1988). Order Restricted Statistical Inference.
23. Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders.
24. Silvapulle, M. J. (1994). On tests against one-sided hypotheses in some generalized linear models. Biometrics 50, 853 858.
25. Silvapulle, M. J. and Sen, P. K. (2005). Constrained Statistical Inference: Inequality, Order, and Shape Restrictions.
26. Silvapulle, M. J., Silvapulle P., and Basawa, I. V. (2002). Tests against inequality constraints in semiparametric models. Journal of Statistical Planning and Inference 107, 307 320.
27. Thomson, A. and Randall-Maciver, R. (1905). Ancient Races of the Thebaid.
28. van der Vaart, A. W. (2000). Asymptotic Statistics.
29. Vardi, Y. (1982). Nonparametric estimation in the presence of length bias. The Annals of Statistics 10, 616 620.
30. Vardi, Y. (1985). Empirical distribution in selection bias models. The Annals of Statistics 13, 178 203.
31. Zelen, M. and Feinleib, M. (1969). On the theory of screening for chronic diseases. Biometrika 56, 601 614.
32. Zhang, B. (2002). Assessing goodness-of-fit of generalized logit models based on case-control data. Journal of Multivariate Analysis 82, 17 38.