Ta. Severini, The likelihood ratio approximation to the conditional distribution of the maximum likelihood estimator in the discrete case, BIOMETRIKA, 87(4), 2000, pp. 939-945
The likelihood ratio approximation, also called Barndorff-Nielsen's approxi
mation and often denoted by p*, provides a highly accurate approximation to
the conditional density of a maximum likelihood estimator <(<theta>)over c
ap> given an ancillary statistic. In this paper, the properties of p* are c
onsidered for the case in which the underlying random variables have a latt
ice distribution and <(<theta>)over cap> has a discrete, but not necessaril
y lattice, distribution. If <(<theta>)over cap> has a lattice distribution,
;then p* provides a valid approximation to the density of <(<theta>)over ca
p> with respect to counting measure. If the distribution of <(<theta>)over
cap> is non-lattice, then p* is still a valid approximation to the conditio
nal density of <(<theta>)over cap> however, the dominating measure is no lo
nger counting measure.