Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory

Journal of Multivariate Analysis

Volumn 101, Issue 9, 2010, Pages 2149-2167

  Ogasawara, Haruhiko ^a  

^a OTARU UNIVERSITY OF COMMERCE   (Japan)

Author keywords

Inverse expansion; Item response theory; Log likelihood derivatives; Pivots; Sandwich estimator

Indexed keywords

EID: 77955053704     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2010.04.001     Document Type: Article

References (29)

1. Abramovitch L., Singh K. Edgeworth corrected pivotal statistics and the bootstrap. Annals of Statistics 1985, 13:116-132.
2. Akahira M., Takeuchi K. On asymptotic deficiency of estimators in pooled samples in the presence of nuisance parameters. Statistics and Decisions 1982, 1:17-38.
3. Andrews D.F., Stafford J.E. Symbolic Computation for Statistical Inference 2000, Oxford University Press, Oxford.
4. Bartlett M.S. Approximate confidence intervals II. More than one unknown parameter. Biometrika 1953, 40:306-317.
5. Bartlett M.S. Approximate confidence intervals. Biometrika 1953, 40:12-19.
6. Beran R. Prepivoting test statistics: a bootstrap view of asymptotic refinements. Journal of the American Statistical Society 1988, 83:687-697.
7. Bock R.D., Lieberman M. Fitting a response model for n dichotomously scored items. Psychometrika 1970, 35:179-197.
8. Bock R.D., Moustaki I. Item response theory in a general framework. Handbook of Statistics: Psychometrics, vol. 26 2007, 469-513. Elsevier, New York. C.R. Rao, S. Sinharay (Eds.).
9. DasGupta A. Asymptotic Theory of Statistics and Probability 2008, Springer, New York.
10. Efron B. Nonparametric standard errors and confidence intervals. The Canadian Journal of Statistics 1981, 9:139-172.
11. Efron B. Better bootstrap confidence intervals. Journal of the American Statistical Society 1987, 82:171-200.
12. Efron B., Hinkley D.V. Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika 1978, 65:457-487.
13. Efron B., Tibshirani R.J. An Introduction to the Bootstrap 1993, Chapman & Hall, New York.
14. Ferguson H. Asymptotic properties of a conditional maximum-likelihood estimator. The Canadian Journal of Statistics 1992, 20:63-75.
15. Hall P. The Bootstrap and Edgeworth Expansion 1992, Springer, New York, Corrected printing, 1997.
16. Hall P. On the removal of skewness by transformation. Journal of the Royal Statistical Society, Series B 1992, 54:221-228.
17. Hayakawa T. The likelihood ratio criterion and the asymptotic expansion of its distribution. Annals of the Institute of Statistical Mathematics 1977, 20A:359-378.
18. Kim S. A sample-based method for obtaining the full variance-covariance matrix of marginal maximum likelihood item parameter estimators. Journal of Educational Evaluation 2008, 21:207-227.
19. Lawley D.N. A general method for approximating to the distribution of likelihood ratio criteria. Biometrika 1956, 43:295-303.
20. Lindsay B.G., Li B. On second-order optimality of the observed Fisher information. The Annals of Statistics 1997, 25:2172-2199.
21. McCullagh P. Tensor Methods in Statistics 1987, Chapman & Hall, London.
22. Ogasawara H. Asymptotic standard errors of IRT equating coefficients using moments. Economic Review (Otaru University of Commerce) 2000, 51(1):1-23. http://www.res.otaru-uc.ac.jp/~hogasa/, http://barrel.ih.otaru-uc.ac.jp/.
23. Ogasawara H. Asymptotic standard errors of IRT observed-score equating methods. Psychometrika 2003, 68:193-211.
24. Ogasawara H. Asymptotic cumulants of the parameter estimators in item response theory. Computational Statistics 2009, 24:313-331. (For errata, see http://www.res.otaru-uc.ac.jp/~hogasa/).
25. Ogasawara H. Inverse transformation of Hall's method back to Edgeworth type expansions: an expository note. New Trends in Psychometrics 2008, 365-370. Universal Academy Press, Tokyo. K. Shigemasu, A. Okada, T. Imaizumi, T. Hoshino (Eds.).
26. Ogasawara H. Some properties of the pivotal statistic based on the asymptotically distribution-free theory in structural equation modeling. Communications in Statistics-Simulation and Computation 2008, 37:1931-1947.
27. J.E. Stafford, Symbolic computation and the comparison of traditional and robust test statistics, Unpublished Doctoral Dissertation, University of Toronto, Canada, 1992.
28. Stuart A., Ord J.K., Arnold S. Kendall's Advanced Theory of Statistics: Classical Inference and the Linear Model 1999, vol. 2A. Arnold, London. 6th ed.
29. Viraswami K., Reid N. Higher-order asymptotics under model misspecification. The Canadian Journal of Statistics 1996, 24:263-278.