Multiple window discrete scan statistics

Journal of Applied Statistics

Volumn 31, Issue 8, 2004, Pages 967-980

  Glaz, Joseph ^a   Zhang, Zhenkui ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Combining test statistics; One dimensional scan statistics; p values; Two dimensional scan statistics; Variable windows

Indexed keywords

EID: 8744298388     PISSN: 02664763     EISSN: None     Source Type: Journal    
DOI: 10.1080/0266476042000270536     Document Type: Article

References (43)

1. Aickin, M. (1983) Serial p-values, Journal of Statistical Planning and Inference, 7, pp. 243-256.
2. Balakrishnan, N. & Koutras, M. V. (2002) Runs and Scans with Applications (New York: Wiley).
3. Berk, R. H. & Cohen, A. (1979) Asymptotically optimal methods for combining tests, Journal of the American Statistical Association 74, pp. 812-814.
4. Berk, R. H. & Jones, D. H. (1978) Relatively optimal combination of test statistics, Scandinavian Journal of Statistics, 5, pp. 158-162.
5. Boutsikas, M. V. & Koutras, M. V. (2000) Reliability approximations for Markov chain imbeddable systems, Methodology and Computing in Applied Probability, 2, pp. 393-412.
6. Crowder, M. (2001) Corrected p-values for tests based on estimated nuisance parameters, Statistical Computing, 11, pp. 359-365.
7. Dodge, Y. & Jurevckova, J. (2002) Adaptive combination of tests, in: Goodness-of-Fit Tests and Model Validity (Paris 2000), pp. 413-424 (Boston, MA: Statistics for Industry and Technology).
8. Dunnett, C. W. (1994) Recent results in multiple testing: several treatments vs. a specified treatment, in: Proceedings of the International Conference on Linear Statistical Inference LINSTAT'93, Mathematics and Its Applications, 306, pp. 35-46 (Dordrecht: Kluwer Academic Publishers).
9. Falk, R. W. (1989) Hommel's Bonferroni-type inequality for unequally spaced levels, Biometrika, 76, pp.189-191.
10. Fu, J. C. (2001) Distributions of scan statistics for a sequence of bi-state trials, Journal of Applied Probability, 38, pp. 1-9.
11. Fu, J. C. & Lou, W. Y. W. (2003) Distribution Theory of Runs and Patterns and its Applications (Singapore: World Scientific Publishing).
12. Glaz, J. & Balakrishnan, N. (Eds) (1999) Scan Statistics and Applications (Boston, MA: Birkhäuser).
13. Glaz, J. & Naus, J. I. (1991) Tight bounds and approximations for scan statistic probabilities for discrete data, Annals of Applied Probability, 1, pp. 306-318.
14. Glaz, J., Naus, J. & Wallenstein, S. (2001) Scan Statistics (New York: Springer-Verlag).
15. Hartung, J. (1999) A note on combining dependent tests of significance, Biometrical Journal, 41, pp.849-855.
16. Hashemi, R. & Commenges, D. (2002) Correction for the p-value after multiple tests in a Cox proportional hazard model, Lifetime Data Analysis, 8, pp. 335-348.
17. Hochberg, Y. (1988) A sharper Bonferroni procedure for multiple tests of significance, Biometrika, 75, pp.800-802.
18. Hochberg, Y. & Rom, D. (1995) Extensions of multiple testing procedures based on Simes' test, Journal of Statistical Planning and Inference, 48, pp. 141-152.
19. Holm, S. (1979) A simple sequentially rejective multiple test procedure, Scandinavian Journal of Statistics, 6, pp. 65-70.
20. Hommel, G. (1988) A stagewise rejective multiple test procedure based on a modified Bonferroni test, Biometrika, 75, pp. 383-386.
21. Hommel, G. (1989) A comparison of two modified Bonferroni procedures, Biometrika, 76, pp. 624-625.
22. Hunter, D. (1976) An upper bound for a probability of a union, Journal of Applied Probability, 13, pp.597-603.
23. Hwang, J. T. G. (2001) An optimality theory for mid p-values in 2 × 2 contingency tables, Statistica Sinica, 11, pp. 807-826.
24. Jennison, C. & Turnbull, B. W. (2000) Group Sequential Methods with Applications to Clinical Trials (Boca-Raton: Chapman & Hall/CRC).
25. Jones, D. H. (1978) Limiting Pitman efficient combination of test statistics, Scandinavian Journal of Statistics, 5, pp. 209-212.
26. Kost, J. T. & McDermott, M. P. (2002) Combining dependent p-values, Statistics & Probability Letters, 60, pp. 183-190.
27. Krauth, J. (1998) Upper bounds for the P-value of a scan statistic with a variable window, in: Classification, Data Analysis, and Data Highways (Potsdam, 1997), pp. 155-163, Study Classification Data Analysis and Knowledge Organization (Berlin: Springer).
28. Kulldorff, M. (1997) A spatial scan statistic, Communication in Statistics - Theory and Methods, 26, pp.1481-1496.
29. Kulldorff, M. (1999) Spatial scan statistics: models, calculations and applications, in: J. Glaz & N. Balakrishnan (Eds) Scan Statistics and Applications, pp. 303-322 (Boston, MA: Birkhauser).
30. Kulldorff, M. & Nagarwalla, N. (1995) Spatial disease clusters: detection and inference, Statistics in Medicine, 14, pp. 799-810.
31. Littell, R. C. & Louv, W. C. (1981) Confidence regions based on methods of combining test statistics, Journal of the American Statistical Association, 76, pp. 125-130.
32. Nagarwalla, N. (1996) A scan statistic with a variable window, Statistics in Medicine, 15, pp. 845-850.
33. Naus, J. I. (1974) probabilities for a generalized birthday problem, Journal of the American Statistical Association, 69, pp. 810-815.
34. Naus, J. I. (1982) Approximations for distributions of scan statistics, Journal of the American Statistical Association, 69, pp. 177-183.
35. Naus, J. I. & Wallenstein, S. (2004) Multiple window and cluster size scan procedures, Methodology and Computing in Applied Probability, 6, pp. 389-400.
36. Nyblom, J. & Pukkila, T. M. (1993) Information criterion as a multiple testing procedure, Journal of Statistical Planning and Inference, 36, pp. 385-397.
37. Pearson, E. S. (1950) On questions raised by the combination of tests based on discontinuous distributions, Biometrika, 37, pp. 383-398.
38. Pozdnyakov, V., Glaz, J., Kulldorff, M. & Steele, J. M. (2004) A martingale approach to scan statistics, Annals of the Institute of Statistical Mathematics, in press.
39. Rom, D. & Holland, B. (1995) A new closed multiple testing procedure for hierarchical families of hypotheses, Journal of Statistical Planning and Inference, 48, pp. 265-275.
40. Simes, R. J. (1986) An improved Bonferroni procedure for multiple tests of significance, Biometrika, 73, pp. 751-754.
41. Wallenstein, S., Naus, J. & Glaz, J. (1994) Power of the scan statistic in detecting a changed segment in a Bernoulli sequence, Biometrika, 81, pp. 595-601.
42. Westfall, P. H. & Young, S. S. (1989) P value adjustments for multiple tests in multivariate binomial models, Journal of the American Statistical Association, 84, pp. 780-786.
43. van de Weil, M. (2001) The split-up algorithm: a fast symbolic method for computing p-values of distribution-free statistics, Computational Statistics, 16, pp. 519-538.