Asymptotic properties of the ANOVA test under general loss functions

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The author studies the classical analysis of variance problem under nonnormal distributions involving a location parameter (so that these distributions really do not involve an unknown variance). The quadratic function in the analysis of variance decomposition is replaced by a convex even function w, and the asymptotic distribution of the corresponding test statistic under the null hypothesis is found to be a chi-squared distribution. Several specific choices of w are considered in detail.