A SYMBOLIC ALGORITHM FOR STUDYING ADJUSTMENTS TO THE PROFILE LIKELIHOOD

A symbolic algorithm for the derivation of the asymptotic expansion of the maximum likelihood estimate was first introduced by Andrews and S tafford (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. E xpansions 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 adj usted likelihood, and asymptotic expansions for the first four moments of the maximum likelihood estimate based on the conditional and adjus ted profile likelihoods, are derived.