Coverage error optimal confidence intervals for local polynomial regression

This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for t statistics and coverage error interval estimators that (i) hold uniformly in the data generating process, (ii) allow uniform kernel, (iii) cover estimation derivatives function. The terms expansions, their associated rates as a function sample size bandwidth sequence, depend on smoothness population function, exploited by procedure, whether evaluation point is interior or boundary support. robust bias corrected confidence intervals have fastest decay all cases, we use our results to deliver novel, inference-optimal selectors. main methodological are implemented companion R Stata software packages.