Gaffke's confidence interval for the mean of bounded data is inadmissible but asymptotically efficient

Jiahao Ming, Aaditya Ramdas, Yi Shen +2

Given observations $\mathbf{x}=(x_1,\dots ,x_n)$, Gaffke (2005) defined \[ K_n(\mathbf x)=\mathbb{P}_{\mathbf D}\!\left\{\sum_{i=1}^n x_iD_i\le 1\right\}, \qquad (D_0,D_1,\ldots,D_n)…