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Large deviations of divergence measures on partitions. (English) Zbl 0996.62052
Summary: We discuss Chemoff-type large deviation results for the total variation, the I-divergence errors, and the \(\chi^2\)-divergence errors on partitions. In contrast to the total variation and the I-divergence, the \(\chi^2\)-divergence has an unconventional large deviation rate. Applications to Bahadur effciencies of goodness-of-fit tests based on these divergence measures for multivariate observations are given.

MSC:
62G20 Asymptotic properties of nonparametric inference
60F10 Large deviations
62G10 Nonparametric hypothesis testing
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