  Samples with a common mean but possibly different, ordered variances arise in
various fields such as interlaboratory experiments, field studies or the
analysis of sensor data. Estimators for the common mean under ordered variances
typically employ random weights, which depend on the sample means and the
unbiased variance estimators. They take different forms when the sample
estimators are in agreement with the order constraints or not, which
complicates even basic analyses such as estimating their variance. We propose
to use the jackknife, whose consistency is established for general smooth
two--sample statistics induced by continuously G\^ateux or Fr\'echet
differentiable functionals, and, more generally, asymptotically linear
two--sample statistics, allowing us to study a large class of common mean
estimators. Further, it is shown that the common mean estimators under
consideration satisfy a central limit theorem (CLT). We investigate the
accuracy of the resulting confidence intervals by simulations and illustrate
the approach by analyzing several data sets.
