Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory
Asymptotic expansions of the distributions of the pivotal statistics involving log-likelihood derivatives under possible model misspecification are derived using the asymptotic cumulants up to the fourth-order and the higher-order asymptotic variance. The pivots dealt with are the studentized ones by the estimated expected information, the negative Hessian matrix, the sum of products of gradient vectors, and the so-called sandwich estimator. It is shown that the first three asymptotic cumulants are the same over the pivots under correct model specification with a general condition of the equalities. An application is given in item response theory, where the observed information is usually used rather than the estimated expected one.
Year of publication: |
2010
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Authors: | Ogasawara, Haruhiko |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 101.2010, 9, p. 2149-2167
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Publisher: |
Elsevier |
Keywords: | Pivots Log-likelihood derivatives Inverse expansion Sandwich estimator Item response theory |
Saved in:
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