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Asymptotically minimax testing ofr>2 simple hypotheses
Authors:V. Kanišauskas
Affiliation:(1) Šiauliai University, Višinskio 25, 5400 Šiauliai, Lithuania
Abstract:In this paper, we consider the problem of asymptotically minimax testing ofr≥2 simple hypotheses when a general stochastic process is observed. We establish general conditions for the exponential decrease of maximal probability errors of minimax tests as the number of observations increases. At the present time, similar results for testing several multinomial schemes were obtained by Salihov [8]. Similar results for testing two simple hypotheses were obtained in [5]. In the proofs of the main results, we use the theory of large deviations ([3], [2]). In Sec. 1, the main result is proved. In Secs. 2–4, we analyze the i.i.d. case, nonhomogeneous Poisson processes, and renewal processes as examples. Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 313–320, July–September, 2000.
Keywords:test  Hellinger integral  rate function  nonhomogeneous Poisson process  renewal process
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