Distribution-Free Lower Bounds in Density Estimation
Distribution-Free Lower Bounds in Density Estimation
We consider the kernel estimate on the real line, $f_n(x) = (nh)^{-1} \sum^n_{i=1} K((X_i - x)/h),$ where $K$ is a bounded even density with compact support, and $X_1, \cdots, X_n$ are independent random variables with common density $f$. We treat the problem of placing a lower bound on the $L$1 …