The Annals of Statistics

The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions

Abstract

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.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 104-113.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346061

Digital Object Identifier
doi:10.1214/aos/1176346061

Mathematical Reviews number (MathSciNet)
MR684868

Zentralblatt MATH identifier
0514.62004

JSTOR