Approximate Interval Probabilities
研究了参数维度为1的模型中，极大似然估计条件分布函数的两种参数化不变近似，分别基于p*公式的偏积分和调整的符号似然比统计量r*，两者在分布尾部也高度一致。
SUMMARY For models of parametric dimension 1 two parameterization invariant approximations to the conditional distribution function of the maximum likelihood estimator are considered. The first is derived by partial integration of a formula for the conditional density given an ancillary statistic (the p*-formula), a technique which in addition yields a useful expression for the error term. For exponential models of order 1 the approximation specializes to the Lugannani–Rice formula. The second approximation is based on an adjusted version (denoted r*) of the signed log-likelihood ratio statistic, which was also derived from p*. These two approximations generally agree closely, even in the far tails of the distribution. A third approximation is a modification of the first that avoids the specification of an ancillary. Some numerical comparisons are given.