A Second-Order Investigation of Asymptotic Ancillarity

摘要: The paper deals with approximate ancillarity as discussed by Efron and Hinkley (1978). In the multivariate i.i.d. case we derive second-order Edgeworth expansion of MLE given a normalized version second derivative log-likelihood at its maximum. agrees one derived Amari (1982a) for curved exponential families, but holds any family satisfying regularity conditions in paper. It is shown that Fisher information lost reducing data to recovered conditioning, it sketched how loss relates deficiency defined LeCam. Finally, investigate some properties three test statistics, proving conjecture (1978) concerning conditional null-distribution likelihood ratio statistic, establishing kind superiority observed over expected estimate inverse variance MLE.