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Zbl 0692.62033
DiCiccio, Thomas J.; Field, Christopher A.; Fraser, D.A.S.
Approximations of marginal tail probabilities and inference for scalar parameters. (English)
[J] Biometrika 77, No.1, 77-95 (1990). ISSN 0006-3444; ISSN 1464-3510/e

Calculation of marginal tail probabilities is central to constructing confidence intervals and testing hypotheses for a scalar parameter. The paper contains two approximations of marginal tail probabilities that are applicable in such situations. For the univariate case the approximations coincide and they are similar to the approximation given by {\it D. A. S. Fraser} [Biometrika 77, 65-76 (1990; see the preceding review, Zbl 0692.62032)]. The errors of both approximations are of $O(n\sp{-3/2})$, where n is the sample size. Numerical results given for conditional inference in location-scale and linear regression models show the approximation to be generally accurate even for small sample sizes.
[D.Rasch]

MSC 2000:: *62F99 Parametric inference
62E99 Statistical distribution theory
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics, etc.
62G15 Nonparametric confidence regions, etc.

Keywords: nuisance parameters; location-scale model; Lugannani-Rice formula; saddlepoint approximation; signed root likelihood ratio statistic; type II censoring; marginal tail probabilities; approximations of marginal tail probabilities; Numerical results; conditional inference; linear regression models

Citations: Zbl 0692.62032

Cited in: Zbl 0926.62019 Zbl 0900.62002 Zbl 0753.62010

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