%0 Journal Article
%T Confidence Regions with Nuisance Parameters
%A Jan Vrbik
%J Open Journal of Statistics
%P 658-675
%@ 2161-7198
%D 2022
%I Scientific Research Publishing
%R 10.4236/ojs.2022.125039
%X 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 </span><i><span style=\"font-family:Verdana;\">all</span></i><span style=\"font-family:Verdana;\"> such parameters, based on the natural logarithm of the
corresponding likelihood function. In this article, we investigate the case of
doing this for only </span><i><span style=\"font-family:Verdana;\">some</span></i><span style=\"font-family:Verdana;\"> 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 </span></span><span><span></span></span><span><span><span style=\"font-family:&quot;\"><span style=\"font-family:Verdana;\">, and further decreasing with 1/</span><i><span style=\"font-family:Verdana;\">n</span></i><span style=\"font-family:Verdana;\">). We provide a general solution to this problem, demonstrating it
by many explicit examples.
%K Confidence Regions
%K Maximum Likelihood
%K Nuisance Parameters
%K Asymptotic Distribution
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=120451