Nonparametric tests for the median from a size-biased sample

Journal of Nonparametric Statistics

Volumn 20, Issue 1, 2008, Pages 19-37

  Kang, Qing ^a   Nelson, Paul I ^b  

^a NORTH DAKOTA STATE UNIVERSITY   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

Asymptotic relative efficiency; Nonparametric test; Permutation test; Size biased sample; Testing median; Weighted distribution

Indexed keywords

EID: 39449113110     PISSN: 10485252     EISSN: 10290311     Source Type: Journal    
DOI: 10.1080/10485250701830113     Document Type: Article

References (22)

1. M. Mahfoud and G.P. Patil, On weighted distributions, in Statistics and Probability: Essay in Honor of CR. Rao, G. Kallianpur, P.R. Krishnaiah and J.K. Ghosh, eds. North-Holland, Amsterdam, 1982.
2. G.P. Patil and C.R. Rao, The weighted distributions: a survey of their applications, in Applications of Statistics, P.R. Krishnaiah eds., North-Holland, Amsterdam, 1977.
3. _, Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics 34 (1978), pp. 179-189.
4. Y. Vardi, Nonparametric estimation in the presence of length bias, Ann. Stat. 7 (1982), pp. 616-620.
5. _, Empirical distributions in selection bias models, Ann. Stat. 13 (1985), pp. 178-203.
6. R.D. Gill, Y. Vardi, and J.A. Wellner, Large sample theory of empirical distributions in biased sampling models, Ann. Stat. 16 (1988), pp. 1069-1112.
7. R.J. Bickel, V.N. Nair, and P.C.C. Wang, Nonparametric inference under biased sampling from afinitì population, Ann. Stat. 20 (1992), pp. 853-878.
8. J. Qin, Empirical likelihood in biased sample problems, Ann. Stat. 21 (1993), pp. 1182-1196.
9. H. El Barmi and M. Rothmann, Nonparametric estimation in selection biased models in the presence of estimating equations, J. Nonparametr. Stat. 9 (1998), pp. 381-399.
10. S. Efromovich, Distribution estimation for biased data, J. Stat. Plann. Inference 124 (2004), pp. 1-43.
11. P.B. Gilbert, S.R. Lele, and Y. Vardi, Maximum likelihood estimation in semipatametric selection bias models with application to AIDS vaccine trials, Biometrika 86 (1999), pp. 27-43.
12. P.B. Gilbert, Large sample theory of maximum likelihood estimates in semiparametric biased sampling models, Ann. Stat. 28 (2000), pp. 151-194.
13. J. Y. Sun and M. Woodroofe, Semi-parametric estimates under biased sampling, Statist. Sinica 7 (1997), pp. 545-575.
14. C.J. Lloyd and M.C. Jones, Nonpammetric density estimation from biased data with unknown biasing function, J. Am. Stat. Assoc. 95 (2000), pp. 865-876.
15. J.A. Cristóbal and J.T. Alcalá, An overview of nonparametric contributions to the problem of functional estimation from biased data, Test 10 (2001), pp. 309-332.
16. J. Navarro, J.M. Ruiz, and Y. Del Aguila, How to detect biased samples? Biomed. J. 45 (2003), pp. 91-112.
17. W. Hoeffding, The large-sample power oftests based on permutations ofobservations, Ann. Math. Stat. 23 (1952), pp. 169-192.
18. J.P. Romano, Bootstrap and randomization tests of some nonparametric hypotheses, Ann. Stat. 17 (1989), pp. 141-159.
19. R.H. Randles and D.A. Wolfe, Introduction to the Theory of Nonparametric Statistics, Krieger Publishing Company, Malabar, 1991.
20. J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978.
21. S.L. Lohr, Sampling: Design and Analysis, Pacific Grove, Duxbury, 1999.
22. Q. Kang, Nonparametric tests of median for a size-biased sample. PhD thesis, Kansas State University, 2005.