A Symbolic Algorithm for Studying Adjustments to the Profile Likelihood
提出一种符号算法，用于推导基于条件、修正或调整剖面似然的最大似然估计的渐近展开，快速获得结果并避免人工错误，从而便于研究三种调整并得到新的统计结论。
A symbolic algorithm for the derivation of the asymptotic expansion of the maximum likelihood estimate was first introduced by Andrews & Stafford (1993). This algorithm is quite general and can be modified to give asymptotic expansions for the maximum likelihood estimate based on either the conditional, modified or adjusted profile likelihoods. Expansions are obtained quickly with no chance for human clerical error. As a result, these three adjustments can be easily studied and some new statistical results are obtained. Bartlett corrections of each adjusted likelihood, and asymptotic expansions for the first four moments of the maximum likelihood estimate based on the conditional and adjusted profile likelihoods, are derived.