I’m curious about this too, not because I’m working on any problems like this, but just because it sounds interesting. I have no insights, but the popular Feldman and Cousins paper about building confidence belts that don’t stray into unphysical ranges might be helpful. Ditto the papers citing that one.
Thank you, that paper contained the solution. The trick is to consider r^2=x’^2+y’^2 as the variable of interest, and note that it may be measured negative; then construct the confidence bands using the ordering principle given in their section III, with a numerical rather than analytical calculation of the likelihood ratios since the probability depends on x’^2 and y’ in a complicated way rather than straightforwardly on the distance from zero. But that’s all implementation details, the concept is exactly what Feldman and Cousins outline.
I’m curious about this too, not because I’m working on any problems like this, but just because it sounds interesting. I have no insights, but the popular Feldman and Cousins paper about building confidence belts that don’t stray into unphysical ranges might be helpful. Ditto the papers citing that one.
Thank you, that paper contained the solution. The trick is to consider r^2=x’^2+y’^2 as the variable of interest, and note that it may be measured negative; then construct the confidence bands using the ordering principle given in their section III, with a numerical rather than analytical calculation of the likelihood ratios since the probability depends on x’^2 and y’ in a complicated way rather than straightforwardly on the distance from zero. But that’s all implementation details, the concept is exactly what Feldman and Cousins outline.
No problem! I was wondering if I was wasting your time with a shot in the dark—glad to hear it helped.