Before revision:  We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal tuning parameter selections we propose. In addition, we show how the large-sample interval length can be further optimized through choice of the kernel function and other tuning parameters. Our main theoretical results rely on novel Edgeworth expansions that are proven to hold uniformly over relevant classes of data generating processes. These higher-order expansions allow for the uniform kernel and any derivative order, improving on previous technical results available in the literature   .
After revision:  We show that robust bias corrected confidence intervals are able to attain the minimax rate when coupled with the principled, inference-optimal bandwidth selectors. The main methodological results are implemented in companion .