Gaussian-efficient testing by betting on the mean of bounded data

Diego Martinez-Taboada, Aaditya Ramdas

Given $[0,1]$-valued random variables $X_1,\dots ,X_n$ such that $\mathbb{E}[X_i|X_1,\dots ,X_{i-1}]=\mu$ for all $i$, we propose a new nonasymptotic confidence interval for $\mu$ tha…