Modeling the variability of rankings

Annals of Statistics

Volumn 38, Issue 5, 2010, Pages 2652-2677

  Hall, Peter ^a   Miller, Hugh ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Bootstrap; Exponential distribution; Exponential tails; Extreme values; Order statistics; Pareto distribution; Performance rankings; Regularly varying tails

Indexed keywords

EID: 77957683077     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AOS794     Document Type: Article

References (23)

1. ALON, U., BARKAI, N., NOTTERMAN, D. A., GISH, K., YBARRA, S., MACK, D. and LEVINE, A. J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc. Natl. Acad. Sci. 96 6745-6750.
2. AMOSOVA, N. N. (1972). Limit theorems for the probabilities of moderate deviations. Vestnik Leningrad. Univ. No. 13 Mat. Meh. Astronom. Vyp. 5-14, 148. MR0331484
3. BARKER, L. E., SMITH, P. J., GERZOFF, R. B., LUMAN, E. T.,MCCAULEY, M.M. and STRINE, T. W. (2005). Ranking states' immunization coverage: An example from the National Immunization Survey. Stat. Med. 24 605-613. MR2134528
4. BRIJS, T., VAN DEN BOSSCHE, F.,WETS, G. andKARLIS, D. (2006). A model for identifying and ranking dangerous accident locations: A case study in Flanders. Statist. Neerlandica 60 457-476. MR2291385
5. BRIJS, T., KARLIS, D., VAN DEN BOSSCHE, F. and WETS, G. (2007). A Bayesian model for ranking hazardous road sites. J. Roy. Statist. Soc. Ser. A 170 1001-1017. MR2408989
6. CESáRIO, L. C. and BARRETO, M. C. M. (2003). Study of the performance of bootstrap confidence intervals for the mean of a normal distribution using perfectly ranked set sampling. Rev. Mat. Estatíst. 21 7-20. MR2058492
7. CHEN, H., STANSY, E. A. andWOLFE, D. A. (2006). An empirical assessment of ranking accuracy in ranked set sampling. Comput. Statist. Data Anal. 51 1411-1419. MR2297530
8. CORAIN, L. and SALMASO, L. (2007). A non-parametric method for defining a global preference ranking of industrial products. J. Appl. Statist. 34 203-216. MR2364253
9. GOLDSTEIN, H. and SPIEGELHALTER, D. J. (1996). League tables and their limitations: Statistical issues in comparisons of institutional performance. J. Roy. Statist. Soc. Ser. A 159 385-443. (Pubitemid 126333152)
10. HALL, P. and MILLER, H. (2009). Using the bootstrap to quantify the authority of an empirical ranking. Ann. Statist. 37 3929-3959. MR2572448
11. HILL, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1174. MR0378204
12. HUI, T. P., MODARRES, R. and ZHENG, G. (2005). Bootstrap confidence interval estimation of mean via ranked set sampling linear regression. J. Stat. Comput. Simul. 75 543-553. MR2162545
13. JOE, H. (2000). Inequalities for random utility models, with applications to ranking and subset choice data. Methodol. Comput. Appl. Probab. 2 359-372. MR1836406
14. JOE, H. (2001). Multivariate extreme value distributions and coverage of ranking probabilities. J. Math. Psych. 45 180-188. MR1820238
15. LANGFORD, I. H. and LEYLAND, A. H. (1996). Discussion of "League tables and their limitations: Statistical issues in comparisons of institutional performance" by Goldstein and Spiegelhalter. J. Roy. Statist. Soc. Ser. A 159 427-428.
16. MCHALE, I. and SCARF, P. (2005). Ranking football players. Significance 2 54-57. MR2224085
17. MEASE, D. (2003). A penalized maximum likelihood approach for the ranking of college football teams independent of victory margins. Amer. Statist. 57 241-248. MR2016258
18. MUKHERJEE, S. N., SYKACEK, P., ROBERTS, S. J. and GURR, S. J. (2003). Gene ranking using bootstrapped p-values. Sigkdd Explorations 5 14-18.
19. MURPHY, T. B. andMARTIN, D. (2003).Mixtures of distance-based models for ranking data. Comput. Statist. Data Anal. 41 645-655. MR1973732
20. NORDBERG, L. (2006). On the reliability of performance rankings. In Festschrift for Tarmo Pukkila on His 60th Birthday (E. P. Liski, J. Isotalo, J. Niemelä and G. P. H. Styan, eds.) 205-216. Univ. Tampere, Tampere, Finland. MR2412962
21. OPGEN-RHEIN, R. and STRIMMER, K. (2007). Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Stat. Appl. Genet. Mol. Biol. 6 Art. 9, 20pp. (electronic). MR2306944
22. QUEVEDO, J. R., BAHAMONDE, A. and LUACES, O. (2007). A simple and efficient method for variable ranking according to their usefulness for learning. Comput. Statist. Data Anal. 52 578-595. MR2410003
23. RÉNYI, A. (1953). On the theory of order statistics. Acta Math. Acad. Sci. Hungar. 4 191-232. MR0061792