A large deviation theorem for the q-sample likelihood ratio statistic
František Rublík · The Annals of Statistics · 1996
An upper bound for the tail probability $P_{\theta} (\log (L(x_{(n_1, \dots, n_q)}, \Theta)/L(x_{(n_1, \dots, n_q)}, \theta)) \geq t)$ is derived in the case of sampling from q populations. This estimate is used for establishing the Hodges-Lehmann optimality of a test statistic for a hypothesis on exponential distributions.