Coverage error optimal confidence intervals for local polynomial regression

By Sebastian Calonico, M. D. Cattaneo, Max H. Farrell. Bernoulli, 2018

69 citations recorded by the source corpus.

In this paper we develop new confidence intervals for local polynomial regression, which minimize their worse-case coverage error and length in large samples. Our results rely on novel, valid Edgeworth expansions for $t$-statistics based on local polynomial methods, which are established uniformly over relevant classes of data generating processes and interval estimators. These higher-order expansions also allow for the uniform kernel and any derivative order, significantly improving on previous technical results available in the literature. In addition, we discuss principled, inference-optimal tuning parameter (bandwidth) selection and kernel functions. The main methodological results obtained in this paper are implemented in companion {\sf R} and \texttt{Stata} software packages.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4ee360a131f7c451facdf2e4235f8e95ea3341c4

Citations in the corpus

• Simple and honest confidence intervals in nonparametric regression (2016, unknown): “If one wants the maximum coverage to be smaller, then undersmoothing (or subtracting an estimate of the bias) will be necessary, and Edgeworth expansions may be needed to deal with higher order approximation terms if one wants α− α→ 0 quickly enough with the sample size (see Calonico et al., 2019).”