@article{toulis2016pivotal,
author = {Panos Toulis},
title = {A useful pivotal quantity},
journal = {The American Statistician},
volume = {71}, year = {2016},
doi = {10.1080/00031305.2016.1237894},
URL = { http://dx.doi.org/10.1080/00031305.2016.1237894 },
eprint = { http://dx.doi.org/10.1080/00031305.2016.1237894 } ,
abstract = {Consider n continuous random variables with joint density f that possibly depends on unknown parameters Î¸. If the negative of the logarithm of f is a positive homogeneous function of degree p taking only positive values, then that function is distributed as a Gamma random variable with shape n/p and scale 2, and thus it is a pivotal quantity for Î¸. This provides a general method to construct pivotal quantities, which are widely applicable in statistical practice, such as hypothesis testing and confidence intervals. Here, we prove the aforementioned result and illustrate through examples. }
}