 
Summary: Confidence regions of fixed volume based on
the likelihood ratio test
Miguel A. Arcones
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 13902, USA
Email: arcones@math.binghamton.edu.
October 26, 2004
Abstract
Assuming that the data comes from a parametric family of d.f.'s, we build confidence
regions for the unknown parameter of a fixed volume based on the likelihood ratio test.
We study the asymptotics of the coverage probability of these regions in two different
situations.
1 Introduction.
We consider the estimation of a finite dimensional parameter. Suppose that a random sample
X1, . . . , Xn from a parametric family {f(x, ) : } of densities in Rd
, is observed, where
is a Borel set of Rd
. We construct confidence regions for with volume bounded by a constant
such that the probability that the confidence region contains the unknown parameter is as
