Statistical inference for P (X < Y)

Statistics in Medicine

Volumn 27, Issue 2, 2008, Pages 257-279

  Zhou, Wang ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Bootstrap; Edgeworth expansions; ROC curve; Stress strength model; The Studentized Wilcoxon Mann Whitney statistics

Indexed keywords

CA 19-9 ANTIGEN; CREATINE KINASE BB;

ACCURACY; ARTICLE; CEREBROSPINAL FLUID ANALYSIS; CONFIDENCE INTERVAL; DISEASE SEVERITY; HEAD INJURY; HUMAN; MATHEMATICAL COMPUTING; MONTE CARLO METHOD; PANCREAS CANCER; PROBABILITY; PROTEIN BLOOD LEVEL; RANDOMIZATION; RANK SUM TEST; STATISTICAL INFERENCE; STATISTICAL MODEL;

CONFIDENCE INTERVALS; DATA INTERPRETATION, STATISTICAL; HUMANS; MEDICINE; MODELS, STATISTICAL; SINGAPORE;

EID: 38849204192     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.2838     Document Type: Article

References (35)

1. Harris B, Soms AP. A note on a difficulty inherent in estimating reliability from stress-strength relationships. Naval Research Logistics Quarterly 1983; 30:659-662.
2. Wolfe DA, Hogg RV. On constructing statistics and reporting data. The American Statistician 1971; 25:27-30.
3. Wilcoxon F. Individual comparisons by ranking methods. Biometrics Bulletin 1945; 1:80-83.
4. Mann HB, Whitney DR. On a test whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics 1947; 18:50-60.
5. Owen DB, Craswell KJ, Hanson DL. Nonparametric upper confidence bounds for P(Y
6. Tong H. On the estimation of P(Y
7. Reiser B, Guttman I. Statistical inference for Pr(Y
8. Pham T, Almhana J. The generalized gamma distribution: its hazard rate and stress-strength model. IEEE Transactions on Reliability 1995; 44:392-397.
9. Gupta CG, Brown N. Reliability studies of the skew-normal distribution and its application to a strength-stress model. Communications in Statistics: Theory and Methods 2001; 30:2427-2445.
10. Johnson RA. Stress-strength models for reliability. In Handbook of Statistics, vol. 7, Krishnaiah PR, Rao CR (eds). Elsevier/ North-Holland: New York/Amsterdam, 1988; 27-54.
11. Kotz S, Lumelskii Y, Pensky M. The Stress-Strength Model and its Generalizations. World Scientific Publishing: New Jersey. 2003.
12. Birnbaum ZW, McCarty BC. A distribution-free upper confidence bounds for Pr(Y
13. Sen PK. On some convergence properties of U-statistics. Calcutta Statistical Association Bulletin 1960; 10:1-18.
14. Sen PK. A note on asymptotically distribution-free confidence intervals for Pr(X
15. 2) based on samples not necessarily independent. Biometrical Journal 1981; 23:627-633.
16. Cheng KF, Chao A. Confidence intervals for reliability from stress-strength relationships. IEEE Transactions on Reliability 1984; 33:246-249.
17. 1
18. Feigin PD, Lumelskii Y, Volkovich ZE. On Monte Carlo simulation of confidence bounds for reliability problems. Proceedings of the 15th European Simulation Multiconference Modelling and Simulation, Prague, 2001; 719-721.
19. Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 1982; 143:29-36.
20. Mee RW. Confidence intervals for probabilities and tolerance regions based on a generalization of the Mann-Whitney statistic. Journal of American Statistical Association 1990; 85:793-800.
21. Newcombe RG. Confidence intervals for an effect size measure based on the Mann-Whitney statistic. Part 1: general issues and tail-area-based methods. Statistics in Medicine 2006; 25:543-557.
22. Newcombe RG. Confidence intervals for an effect size measure based on the Mann-Whitney statistic. Part 2: asymptotic methods and evaluation. Statistics in Medicine 2006; 25:559-573.
23. Alberink IB. A Berry-Esseen bound for U-statistics in the non-i.i.d, case. Journal of Theoretical Probability 2000; 13:519-533.
24. Petrov VV. Sums of Independent Random Variables. Springer: Berlin, 1975.
25. Bickel PJ, Götze F, van Zwet WR. The Edgeworth expansion for U-statistics of degree two. Annals of Statistics 1986; 14 :1463-1484.
26. Bentkus V, Götze F, van Zwet WR. An Edgeworth expansion for symmetric statistics. Annals of Statistics 1997; 25:851-896.
27. Jing BY, Zhou W. A note on Edgeworth expansion for U-statistics under minimal conditions. Lithuanian Mathematical Journal 2005; 45:353-358.
28. Efron B. Bootstrap methods: another look at the jacknife. Annals of Statistics 1979; 7:1-26.
29. Hall P. The Bootstrap and Edgeworth Expansion. Springer: New York, 1992.
30. Singh K. On asymptotic accuracy of Efron's bootstrap. Annals of Statistics 1981; 9:1187-1195.
31. Arvesen JN. Jackknifing U-statistics. Annals of Mathematical Statistics 1969; 40:2076-2100.
32. Press WH, Flannery BF, Teukolsky SA, Vetterling WT. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press: Cambridge, MA, 1989.
33. Wieand S, Gail MH, James BR, James KL. A family of nonparametric statistics for comparing diagnostic markers with paired and unpaired data. Biometrika 1989; 76:585-592.
34. Hans O, Albert A, Born J, abd Chapelle J. Derivation of a bioclinical index in severe head trauma. Intensive Care Medicine 1985; 11:186-191.
35. Maesono Y. Edgeworth expansion for two-sample U-statistics. Reports of the Faculty of Science, vol. 18, Kagoshima University, Mathematics, Physics and Chemistry 1985; 35-43.