Asymptotics when the number of parameters tends to infinity in the Bradley-Terry model for paired comparisons

Annals of Statistics

Volumn 27, Issue 3, 1999, Pages 1041-1060

  Simons, Gordon ^a   Yao, Yi Ching ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Bradley Terry model; Central limit theorem; Consistency; Fisher information matrix; Maximum likelihood estimator

Indexed keywords

EID: 0033248630     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (20)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. BRADLEY, R. A. (1954). Incomplete block rank analysis: on the appropriateness of the model for a method of paired comparisons. Biometrics 10 375-390.
3. BRADLEY, R. A. (1955). Rank analysis of incomplete block designs III. Some large-sample results on estimation and power for a method of paired comparisons. Biometrika 42 450-470.
4. BRADLEY, R. A. and TERRY, M. E. (1952). The rank analysis of incomplete block designs I. The method of paired comparisons. Biometrika 39 324-345.
5. BÜHLMANN, H. and HUBER P. J. (1963). Pairwise comparisons and ranking in tournaments. Ann. Math. Statist. 34 501-510.
6. COLONIUS, H. (1980). Representation and uniqueness of the Bradley-Terry-Luce model for pair comparisons. British J. Math. Statist. Psych. 33 99-103.
7. DAVID, H. A. (1988). The Method of Paired Comparisons, 2nd ed. Griffin, London.
8. DAVIDSON, R. R. and FARQUHAR, P. H. (1976). A bibliography on the method of paired comparisons. Biometrics 32 241-252.
9. FORD, L. R., JR. (1957). Solution of the ranking problem from binary comparisons. Amer. Math. Monthly 64 28-33.
10. HOEFFDING, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 13-30.
11. JECH, T. (1983). The ranking of incomplete tournaments: a mathematician's guide to popular sports. Amer. Math. Monthly 90 246-266.
12. LOÈVE, M. (1963). Probability Theory, 3rd ed. Van Nostrand, New York.
13. NEYMAN, J. and SCOTT, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica 16 1-32.
14. 2/n is large I. Consistency. Ann. Statist. 12 1298-1309.
15. 2/n is large II. Normal approximation. Ann. Statist. 13 1403-1417.
16. PORTNOY, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. Ann. Statist. 16 356-366.
17. SIMONS, G. and YAO, Y.-C. (1998). Approximating the inverse of a symmetric positive definite matrix. Linear Algebra Appl. 281 97-103.
18. STOB, M. (1984). A supplement to "Mathematician's Guide to Popular Sports." Amer. Math. Monthly 91 277-282.
19. SUPPES, P. and ZINNES, J. L. (1963). Basic measurement theory. In Handbook of Mathematical Psychology (R. D. Luce, R. R. Bush and E. Galanter, eds.) 1 1-76. Wiley, New York.
20. ZERMELO, E. (1929). Die Berechnung der Turnier-Ergebnisse als ein Maximumproblem der Wahrscheinlichkeitsrechnung. Math. Zeit. 29 436-460.