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.
Publié le : 1983-03-14
Classification:
Ancillary statistics,
conditional inferences,
confidence intervals for parametric functions,
pivotal quantities,
robust,
62A99,
62F35
@article{1176346061,
author = {Barnard, G. A. and Sprott, D. A.},
title = {The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 104-113},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346061}
}
Barnard, G. A.; Sprott, D. A. The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions. Ann. Statist., Tome 11 (1983) no. 1, pp. 104-113. http://gdmltest.u-ga.fr/item/1176346061/