Semi-parametric estimates under biased sampling

Statistica Sinica

Volumn 7, Issue 3, 1997, Pages 545-575

  Sun, Jiayang ^a,b   Woodroofe, Michael ^a,b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Animal and oil data; Consistency; Convergence; EM algorithm; Incomplete sample; Maximum likelihood estimates; MM algorithm; Selection bias; Simulations

Indexed keywords

EID: 0031486567     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Bickel, P. J., Nair, V. N. and Wang, P. C. C. (1992). Nonparametric inference under biased sampling from a finite population. Ann. Statist. 20, 853-878.
2. Bloomfield, P., Deffeyes, K. S., Silverman, B., Watson, G. S., Benjamini, Y. and Stine, R. A. (1979). Volume and area of oil fields and their impact on order of discovery. Resource Estimation and Validation Project, Department of Statistics and Geology, Princeton University.
3. Breslow, N. E. and Day, N. E. (1980). Statistical Methods in Cancer Research. Lyon : International Agency for Research on Cancer.
4. Brown, L. D. (1986). Fundamentals of Statistical Exponential Families: with Applications in Statistical Decision Theory. Hayward, Calif. Institute of Mathematical Statistics.
5. Cook, R. D. and Martin, F. B. (1974). A model for quadrat sampling with "visibility bias". J. Amer. Statist. Assoc. 69, 345-349.
6. Csörgo, M. and Revesz, P. (1981). Strong Approximation in Probability and Statistics. Academic Press.
7. Gill, R. D., Vardi, Y. and Wellner, J. A. (1988). Large sample theory of empirical distributions in biased sampling models. Ann. Statist. 16, 1069-1112.
8. Groeneboom, P. (1985). Estimating a monotone density. In Proc. Conf. in Honor of Jerzy Neyman and Jack Kiefer 2 (Edited by L. M. LeCam and R. A. Olshen), 539-555.
9. Groeneboom, P. and Pyke, R. (1983). Asymptotic normality of statistics based on the convex minorants of empirical distribution functions. Ann. Probab. 11, 328-345
10. Good, I. J. and Gaskins, R. A. (1971). Nonparametric roughness penalties for probability densities. Biometrika 58, 255-277.
11. Gordon, L. (1993). Estimation for large successive samples with unknown inclusion probabilities. Adv. Appl. Math. 14, 89-122.
12. Lynden-Bell, D. (1993). Eddington-Malmquist bias, streaming motions, and the distribution of galaxies. In Statistical Challenges in Modern Astronomy (Edited by G. J. Babu and E. D. Feigelson), 201-220.
13. Manski, C. F. (1993). The selection problem in econometrics and statistics. In Econometrics (Edited by G. S. Maddala, C. R. Rao and H. D. Vinod), 73-84. Amsterdam; North-Holland, New York.
14. Meisner, J. and Demirmen F. (1981). The creaming method: a Bayesian procedure to forecast future oil and gas discoveries in mature exploration provinces. J. Roy. Statist. Soc. Ser. A. 144, 1-31.
15. Patil, G. P. and Rao, C. R. (1976). The weighted distributions: a survey of their applications. In Applications of Statistics. Proceedings of the symposium held at Wright State University, Dayton, Ohio, 14-18 June 1976 (Edited by P. R. Krishnaiah), 383-405. North-Holland, Amsterdam.
16. Robertson, T., Wright, F. and Dykstra R. (1988). Order Restricted Inference. John Wiley.
17. Robbins, H. and Zhang, C. H. (1988). Estimating a treatment effect under biased sampling. Proc. Nat. Acad. Sci. 85, 3670-3672.
18. Silverman, B. W. (1986). Density Estimation. Chapman and Hall.
19. Vardi, Y. (1982). Nonparametric estimation in the presence of length bias. Ann. Statist. 10, 616-620.
20. Vardi, Y. (1985). Empirical distributions in selection bias models. Ann. Statist. 13, 178-205.
21. Vardi, Y. and Zhang, C. H. (1992). Large sample study of empirical distributions in a random-multiplicative censoring model. Ann. Statist. 20, 1022-1039.
22. Woodroofe, M. (1993). Discussion of "Eddington Malmquist bias, streaming motions, and the distribution of galaxies". In Statistical Challenges in Modern Astronomy (Edited by G. J. Babu and E. D. Feigelson), 217-220.
23. Woodroofe, M. and Sun, J. (1993). A penalized maximum likelihood estimate of f(0+) when f is non-increasing. Statist. Sinica 3, 501-515.
24. Sun, J. and Woodroofe, M. (1996). Adaptive smoothing for a penalized npmle of a non-increasing density. J. Statist. Plann. Inference 52, 143-159.
25. Wu, C. F. J. (1983). Convergence properties of the EM algorithm. Ann. Statist. 11, 95-103.