On Three Hypotheses Robust Detection Design Under Mismatch

Generalizing the result of D. Kazacos for two hypotheses we consider the ternary detection problem of the Neyman-Pearson type under mismatch. For the case of independent identically distributed observations the sufficiency condition of existence of test with an exponentially dicreasing probability of error is formulated in terms of the new notion of “divergence for three distributions in certain order”.