TITLE:
Confidence Regions with Nuisance Parameters
AUTHORS:
Jan Vrbik
KEYWORDS:
Confidence Regions, Maximum Likelihood, Nuisance Parameters, Asymptotic Distribution
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.5,
October
18,
2022
ABSTRACT: Consider a distribution with several parameters whose exact values are
unknown and need to be estimated using the maximum-likelihood technique. Under
a regular case of estimation, it is fairly routine to construct a confidence
region for all such parameters, based on the natural logarithm of the
corresponding likelihood function. In this article, we investigate the case of
doing this for only some of these parameters, assuming that the
remaining (so called nuisance) parameters are of no interest to us. This is to
be done at a chosen level of confidence, maintaining the usual accuracy of this
procedure (resulting in about 1% error for samples of size , and further decreasing with 1/n). We provide a general solution to this problem, demonstrating it
by many explicit examples.