Unknown Variance

Unknown variance in statistical models presents a significant challenge across various fields, demanding robust methods for estimation and inference. Current research focuses on developing asymptotically optimal algorithms for best-arm identification and constructing confidence sequences for Gaussian means, often leveraging techniques like Neyman allocation and adaptive sampling strategies to account for the unknown variance. These advancements improve the accuracy and efficiency of statistical procedures in settings where the variance is not known a priori, impacting fields ranging from online learning to clinical trials. The development of finite-sample guarantees and the exploration of connections to Fisher information further refine our understanding and application of these methods.