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March, 1983 The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions
G. A. Barnard, D. A. Sprott
Ann. Statist. 11(1): 104-113 (March, 1983). DOI: 10.1214/aos/1176346061


The pivotal model is described and applied to the estimation of parametric functions $\phi(\theta)$. This leads to equations of the form $H(x; \theta) = G\{p(x, \theta)\}$. These can be solved directly or by the use of differential equations. Examples include various parametric functions $\phi(\theta, \sigma)$ in a general location-scale distribution $f(p), p = (x - \theta)/\sigma$ and in two location-scale distributions. The latter case includes the ratio of the two scale parameters $\sigma_1/\sigma_2$, the difference and ratio of the two location parameters $\theta_1 - \theta_2$ and the common location $\theta$ when $\theta_1 = \theta_2 = \theta$. The use of the resulting pivotals to make inferences is discussed along with their relation to examples of non-uniqueness occurring in the literature.


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G. A. Barnard. D. A. Sprott. "The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions." Ann. Statist. 11 (1) 104 - 113, March, 1983.


Published: March, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0514.62004
MathSciNet: MR684868
Digital Object Identifier: 10.1214/aos/1176346061

Primary: 62A99
Secondary: 62F35

Keywords: Ancillary statistics , conditional inferences , confidence intervals for parametric functions , pivotal quantities , robust

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • March, 1983
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