Successive improvement of the order of ancillarity

摘要: SUMMARY It is shown by an argument similar to one of Welch (1947) that it is, under usual regularity conditions, in general possible improve the order ancillarity successively. This means when asymptotic ancillary has been constructed, such its distribution independent parameter apart from terms O(n- k), then a new may be constructed with which depends on only through O(nk22). how explicitly expansion Edgeworth type, more specifically normal density multiplied linear combinations Hermite polynomials.