Abstract
Asymptotically efficient tests satisfying a minimax type criterion are derived for testing composite hypotheses involving several parameters in nonergodic type stochastic processes. It is shown, in particular, that the analogue of the usual Neyman's C (α) type test (i.e., the score test) is not efficient for the nonergodic case. Moreover, the likelihood-ratio statistic is not fully efficient for the model discussed in the paper. The efficient statistic derived here is a modified version of the score-statistic discussed previously by Basawa and Koul (1979).
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