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An Edgeworth expansion for $$U$$-statistics with weakly dependent observations. (English) Zbl 0841.62010
Summary: Under mild conditions, an Edgeworth expansion with remainder $$o(N^{-1/2})$$ is established for a $$U$$-statistic with a kernel $$h$$ of degree two using weakly dependent observations. The case of verifying these conditions is discussed in the context of three rather natural examples.
##### MSC:
 62E20 Asymptotic distribution theory in statistics 60G15 Gaussian processes 62M99 Inference from stochastic processes 60G10 Stationary stochastic processes