Likelihood computations without Bartlett identities

The signed square root statistic R is given by sgn(<(<theta>)over cap> - th eta)(l(<(<theta>)over cap>)- l(theta))(1/2), where l is the log-likelihood and <(<theta>)over cap> is the maximum likelihood estimator. The pth cumula nt of R is typically of the form n(-p/2)k(p) + O(n(-(p+2)/2)), where n is t he number of observations. This paper shows how to symbolically compute k(p ) without invoking the Bartlett identities. As an application, we show how the family of alternatives influences the coverage accuracy of R.