Choosing the $p$ in $L_p$ loss: rate adaptivity on the symmetric location problem

Yu-Chun Kao, Min Xu, Cun-Hui Zhang

Given univariate random variables $Y_1,\dots ,Y_n$ with the $\text{Uniform}({\theta }_0-1,{\theta }_0+1)$ distribution, the sample midrange $\frac{Y_{(n)}+Y_{(1)}}{2}$ is the MLE for ${\theta }_0$…