Edgeworth expansions for statistics which are functions of lattice and non-lattice variables

Let G be a distribution function on Iw’+’ such that the (k + 1)th marginal is lattice. Let 2, denote the sampe mean of n independent observations from G. For s > 3, the s-term Edgeworth expansions are obtained for a wide class of statistics which are smooth functions of 2,. The result is then applied to a statistic similar to the Student’s t-statistic, where the scaling factor, the sample standard deviation is replaced by the more robust mean absolute deviation. AMS 1980 Subject Classification: 62B20