Confidence Intervals for Nonparametric Regression

In non-parametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James-Stein shrinkage estimator; the other begins with a Bayesian perspective and is based on a modification of the harmonic prior estimator. Simulation shows that these confidence intervals have average coverage close to or above the nominal coverage even when the underlying function is rough and/or the signal to noise ratio is small. Both of the confidence intervals perform consistently well across all the investigated test functions even through these functions have very different shapes and smoothness.