Jackknifing Maximum Likelihood Estimates

Abstract

This paper proves the apparently outstanding conjecture that the maximum likelihood estimate (m.l.e.) "behaves properly" when jackknifed. In particular, under the usual Cramer conditions (1) the jackknifed version of the consistent root of the m.l. equation has the same asymptotic distribution as the consistent root itself, and (2) the jackknife estimate of the variance of the asymptotic distribution of the consistent root is itself consistent. Further, if the hypotheses of Wald's consistency theorem for the m.l.e. are satisfied, then the above claims hold for the m.l.e. (as well as for the consistent root).