Nonparametric Confidence Intervals

By G. E. Noether. 2006

101 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/176779d4e380b9a82ab0e4cb18b5624cc317ae8d

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Citations in the corpus

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]).”
On adaptive posterior concentration rates (2013, background): “The behaviour of such a pair (ℓ, d) is reminiscent of several phenomena in the minimax nonparametric literature: these include estimation of linear functionals Donoho and Liu [15], constrained risk inequalities Brown and Low [5], Cai and Low [9], Cai et al. [8] or the existence of adaptive confidenc”
An adaptation theory for nonparametric confidence intervals (2004, background): “Low (1997) has given examples where L∗α(F1,F)≫ L∗α(F1), in which case strongly adaptive estimators do not exist.”
Anti-concentration and honest, adaptive confidence bands (2013, background): “, if F = (t,L)∪ (t ′,L) for t ′ > t], the construction of honest adaptive confidence bands is not possible; see [33].”
Inference in Regression Discontinuity Designs with a Discrete Running Variable (2016, methodology): “To show that the amount of under-coverage can be substantial, we re-analyze data from Oreopoulos (2006), and find that EHW standard errors are larger than CRV standard errors by several orders of magnitude in this context, with the exact amount depending on the precise specification. The exercise sh”
On adaptive inference and confidence bands (2011, background): “THEOREM 1 (Low).”
Simple and honest confidence intervals in nonparametric regression (2016, methodology): “While this may appear to be a disadvantage of our particular approach, due to impossibility results of Low (1997), Cai and Low (2004), and Armstrong and Kolesár (2018a), this cannot be avoided, regardless of how one forms the CI, without making further restrictions on the function f .”
CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, background): “48 01 v1 [ m at h. ST ] 2 5 Fe b 20 10 The Annals of Statistics 2010, Vol. 38, No. 2, 1122–1170 DOI: 10.1214/09-AOS738 c© Institute of Mathematical Statistics, 2010”
Multivariate and univariate asymmetrical analyses in environmental impact assessment: a case study of Mediterranean subtidal sessile assemblages (2005, methodology): “It is also a distribution-free method in that estimation and inference is based on a statistic whose distribution does not depend in any way on complete specification of the distributions of the species variables (Gibbons 1982, Noether 1985).”
Optimal inference in a class of regression models (2015, methodology): “(2004a), who consider confidence sets that take the form of a two-sided CI, and, subject to coverage over F , derive bounds on the maximum expected length over G, and the results in Cai, Low, and Xia (2013), who obtain bounds on the expected length of two-sided CIs at a single function g.”
Confidence sets for nonparametric wavelet regression (2005, methodology): “This is consistent with the results in Low (1997) and Cai and Low (2003) that suggest confidence sets cannot be rate adaptive.”