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We take into account the leaving\u2010one\u2010out cross\u2010validation (CV) when determining the optimum tuning parameters and bootstrapping the deviance in order to summarize the measure of goodness\u2010of\u2010fit in SVMs. The leaving\u2010one\u2010out CV is also adapted in order to provide estimates of the bias of the excess error in a prediction rule constructed with training samples. 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