The classical hypothesis testing problem involves, given n samples, to decide whether they were sampled from a distribution p or distribution q. Here we consider the case when the actual distributions p and q are unknown; it is only known p is close to p_0 and q to q_0 (in KL divergence sense). We will find the optimal test, optimal probability of error and the worst case distribution, for certain types of p_0,q_0.
Based on a paper with the same title by Bernard Levy.
