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Hellinger integrals, error probabilities, and contiguity of Gaussian processes with independent increments and Poisson processes. (English) Zbl 0582.62075

Hellinger integrals with a complex parameter are introduced and determined for Gaussian processes with independent increments and Poisson processes. As an application the distribution of the log-likelihood ratio for these processes is obtained.
Furthermore, the error probabilities in hypotheses testing problems are calculated or estimated, resp. contiguous and entirely separated sequences of distributions are characterized with the aid of Hellinger integrals.

MSC:

62M02 Markov processes: hypothesis testing
62F03 Parametric hypothesis testing
62E15 Exact distribution theory in statistics
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