Simple and accurate one-sided inference from signed roots of likelihood ratios

The authors propose two methods based on the signed root of the likelihood ratio statistic for one-sided testing of a simple null hypothesis about a scalar parameter in the presence of nuisance parameters. Both methods are third-order accurate and utilise simulation to avoid the need for onerous analytical calculations characteristic of competing saddlepoint procedures. Moreover, the new methods do not require specification of ancillary statistics. The methods respect the conditioning associated with similar tests up to an error of third order, and conditioning on ancillary statistics to an error of second order.