| Autor: |
Gatto, Riccardo, Ronchetti, Elvezio |
| Předmět: |
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| Zdroj: |
Journal of the American Statistical Association; Jun96, Vol. 91 Issue 434, p666-673, 8p, 2 Charts, 6 Graphs |
| Abstrakt: |
The article presents a derivation of saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics. Saddlepoint techniques are useful tools to derive very accurate approximations of densities and tail probabilities. The authors' procedure has three key ingredients First, an expansion of the statistic up to the second order is needed. The expression can be viewed as a U statistic of Therefore, we can use the available expressions for the cumulants given in Step 2. The final ingredient in Step 3 is the general saddlepoint approximation of the density and tail area of a univariate statistic when approximations for the first four cumulants are available. In Section 2 the authors derive our basic approximation and discuss some related approximations. In Section 3 they apply their approximation to a variety of models and estimators, including the maximum likelihood estimator for the parameters in regular logit and probit models and the R estimators in linear models. Small simulation studies and examples based on real data show the accuracy and the generality of their approximation. |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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