Adaptive confidence bands

By Christopher R. Genovese, Larry A. Wasserman. 2007

62 citations recorded by the source corpus.

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f* which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f* and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.

Subfields: Computer Vision and Pattern Recognition, Statistics and Probability

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “The latter additional requirement means that the inference on perfectly localized functionals is less robust than the inference on the local functionals (analogously, to the point that was made by Genovese and Wasserman (2008)).”
CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, background): “Genovese and Wasserman (2008) revisit the negative results by Low (1997) in the framework of regression.”
On adaptive inference and confidence bands (2011, background): “It follows from Theorem 2 in Low [26] (see also [4, 8]) that such bands do not exist.”
Generic Machine Learning Inference on Heterogenous Treatment Effects in Randomized Experiments (2017, unknown): “,[17]), inference remains a more difficult problem, as adaptive confidence sets do not exist even for low-dimensional nonparametric problems ([41, 29]).”
Honest adaptive confidence bands and self-similar functions (2011, methodology): “Different conditions have been considered by Picard and Tribouley (2000), Genovese and Wasserman (2008), Giné and Nickl (2010), and Hoffmann and Nickl (2011).”
Local and global asymptotic inference in smoothing spline models (2012, background): “When h is chosen as the above upper bound and dn √logn, our SCB achieves the minimum order of bandwidth n−m/(2m+1)(logn)(m+1)/(2m+1), which turns out to be optimal according to [12].”
Distribution‐free prediction bands for non‐parametric regression (2014, background): “Another important class of methods is quantile regression (Koenker and Hallock, 2001) where it is assumed, in a non-parametric form, that the τ th quantile of Y given X=x is a smooth function fτ .x/. If such a quantile regression assumption holds for both τ =α=2 and τ =1−α=2, then a prediction band ”