Third order asymptotics: connections among test quantities |
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Authors: | P.K. Cheah D.A.S. Fraser N. Reid A. Tapia |
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Affiliation: | 1. Department of Statistics , University of Toronto , Toronto, M5S 1Al, Canada;2. Department of Mathematics and Statistics , York University , North York, M3J 1P3, Canada;3. Department of Statistics , University of Toronto , Toronto, M5S 1A1, Canada |
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Abstract: | Saddlepoint methods, extended to distribution functions, can provide highly accurate tail probabilities for testing real parameters in exponential models. For extensions, asymptotic connections among various test quantities are needed. For five quantities, the maximum likelihood departure standardized by observed and expected information, the score function standardized by observed and expected information, and the signed square root of the likelihood ratio statistic, the needed connections to third order are recorded. Their use is illustrated by a simple integration proof of the Lugannani and Rice formula. |
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Keywords: | asymptotic approximations exponential model saddlepoint approximation tail probabilities test quantities |
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