Likelihood Computations without Bartlett Identities

摘要

The signed square root statistic R typically has cumulants on the form cum(p)(R)= theta(2,p) + n(-p/2)Kp + On(-(p+2)/2). This paper shows how to compute Kp without invoking the Bartlett identities. As an application, we show how the family of alternatives influences the coverage accuracy of R, and in particular that a bad choice of family can lead to arbitrary undercoverage for confidence intervals based on R.