We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for mean univariate distribution. By utilizing geometric interpretation GLR statistic, we derive simple analytic upper bound on probability that it exceeds any prespecified boundary; these are intractable to approximate via simulations due infinite h...

This paper studies the Generalized Neyman–Pearson (GNP) optimality of empirical likelihood-based tests for parameter hypotheses. The GNP optimality focuses on the large deviation errors of tests, i.e., the convergence rates of the type I and II error probabilities under fixed alternatives. We derive (i) the GNP optimality of the empirical likelihood criterion (ELC) test against all alternatives...