Robust Sequential Tests for Memoryless Discrimination from Dependent Observations

Abstract

The problem of robust sequential discrimination from two dependent observation sequences with uncertain statistics is addressed. As in Part I ([1]) of this study, which treated asymptotically optimal sequential discrimination for stationary observations characterized by m - dependent or mixing type of dependence, sequential tests based on memoryless nonlinearities are employed. In particular, the sequential tests robustified in this paper employ linear test _ n _ n, statistics of the form Sn = A g (Xi ) + Bn, , where {Xi } i = 1 is the observation _ i = 1 _, sequence, the coefficients A and B are selected so that the normalized drifts of S n are antipodal under the two hypotheses, and the nonlinearity g solves a linear integral equation. As shown in Part I, the performance of these tests is very close to that of the asymptotically optimal memoryless sequential tests when the statistics of the observations are known. The above tests are robustified in terms of the error probabilities and the expected sample numbers under the two hypotheses, for statistical uncertainty determined by 2-alternating capacity classes for the marginal (univariate) pdfs and upper bounds on the correlation coefficients of time-shifts of the observations sequence for the bivariate pdfs. Finally, the robustification of sequential tests based on a test statistic similar to Sn defined above is carried out for detecting a weak-signal in stationary m - dependent or mixing noise with uncertainty in the univariate and bivariate pdfs.