Abstract
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.
Citation
František Rublík. "A large deviation theorem for the q-sample likelihood ratio statistic." Ann. Statist. 24 (5) 2280 - 2287, October 1996. https://doi.org/10.1214/aos/1069362322
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