(Received September 25, 1992; revised April 27, 1993)
Abstract. This paper contains two results. The first establishes, under mild assumptions, the validity of an Edgeworth expansion with remainder o( N -1/2) for a U-statistic with a kernel of degree two using observations from an m-dependent shift. The second result gives a necessary and sufficient condition for the distribution of a sum of m-dependent random variables to possess an Edgeworth expansion. This generalizes a result of Bickel and Robinson from the i.i.d. case to the m-dependent case.
Key words and phrases: Edgeworth expansions, U-statistics, m-dependence.
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