Nonparametric Confidence Sets for Functions
10 May 2023 09:49
Yet another inadequate placeholder, for an important technical topic in statistics. (I don't work on it, but I need to understand it better than I do.) In particular, I cannot give you a good, intuitive explanation for why "just bootstrap" doesn't work.
See also: Confidence Sets
- Recommended:
- Christopher R. Genovese and Larry Wasserman
- "Confidence sets for nonparametric wavelet regression", Annals of Statistics 33 (2005): 698--729, math.ST/0505632
- "Adaptive Confidence Bands", Annals of Statistics 36 (2008): 875--905, math.ST/0701513
- Evarist Giné and Richard Nickl, Mathematical Foundations of Infinite-Dimensional Statistical Models
- Peter Hall, "On Bootstrap Confidence Intervals in Nonparametric Regression", Annals of Statistics 20 (1992): 695--711
- Peter Hall and Joel Horowitz, "A simple bootstrap method for constructing nonparametric confidence bands for functions", Annals of Statistics 41 (2013): 1892--1921, arxiv:1309.4864
- To read:
- Timothy B. Armstrong, Michal Kolesár, "Simple and Honest Confidence Intervals in Nonparametric Regression", arxiv:1606.01200
- Andrii Babii, "Honest Confidence Sets in Nonparametric IV Regression and Other Ill-Posed Models", Econometric Theory 36 2020: 658--706, arxiv:1611.03015
- Adam D. Bull, "Honest adaptive confidence bands and self-similar functions", Electronic Journal of Statistics 6 (2012): 1490--1516, arxiv:1110.4985
- Adam D. Bull, Richard Nickl, "Adaptive confidence sets in $L^2$", Probability Theory and Related Fields 156 (2013): 889--919
- T. Tony Cai, "Minimax and Adaptive Inference in Nonparametric Function Estimation", Statistical Science 27 (2012): 31--50
- T. Tony Cai and Mark G. Low, "An adaptation theory for nonparametric confidence intervals", Annals of Statistics 32 (2004): 1805--1840, math.ST/0503662 ,
- Victor Chernozhukov, Denis Chetverikov, and Kengo Kato, "Anti-concentration and honest, adaptive confidence bands", Annals of Statistics 42 (2014): 1787--1818, arxiv:1303.7152
- P. L. Davies, A. Kovac and M. Meise, "Nonparametric Regression, Confidence Regions and Regularization", arxiv:0711.0690
- Lutz Duembgen, Jon A. Wellner, "Confidence Bands for Distribution Functions: A New Look at the Law of the Iterated Logarithm", arxiv:1402.2918
- Heng Lian, "Empirical Likelihood Confidence Intervals for Nonparametric Functional Data Analysis", arxiv:0904.0843
- Marc Hoffmann and Richard Nickl, "On adaptive inference and confidence bands", Annals of Statistics 39 (2011): 2383--2409
- Matthieu Lerasle, "Adaptive non-asymptotic confidence balls in density estimation", arxiv:1007.4528 `
- James Robins and Aad van der Vaart, "Adaptive nonparametric confidence sets", Annals of Statistics 34 (2006): 229--253, arxiv:math/0605473 ["We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models."]
