Higher-order Bartlett-type adjustment

This paper deals with Bartlett-type adjustment which makes all the terms up to order n(-k) in the asymptotic expansion vanish, where k is an integer k greater than or equal to 1 and n depends on the sample size. Extending Cordeiro and Ferrari (1991, Biometrika, 78, 573-582) for the case of k = 1, we derive a general formula of the kth-order Bartlett-type adjustment for the test statistic whose kth-order asymptotic expansion of the distribution is given by a finite linear combination of chi-squared distribution with suitable degrees of freedom. Two examples of the second-order Bartlett-type adjustment are given. We also elucidate the connection between Bartlett-type adjustment and Cornish-Fisher expansion. (C) 1997 Elsevier Science B.V.