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

Haruhiko Ogasawara

Journal of Multivariate Analysis, 2010, vol. 101, issue 9, 2149-2167

Abstract: 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.

Keywords: Pivots; Log-likelihood; derivatives; Inverse; expansion; Sandwich; estimator; Item; response; theory (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (9)

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