Adaptive confidence interval for pointwise curve estimation

By Dominique Picard, Karine Tribouley. 2000

109 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/adc7f15a2a55d1fb244528383344179e1304cf22

Citations in the corpus

• Honest adaptive confidence bands and self-similar functions (2011, unknown): “Similar conditions have been considered by previous authors, in the context of turbulence by Frisch and Parisi (1985) and Jaffard (2000), and more recently in statistical applications by Picard and Tribouley (2000) and Giné and Nickl (2010).”
• Adaptive confidence sets in $$L^2$$ (2011, unknown): “One way to remove is to restrict the space a priori to a fixed ball (r, B0) of known radius as discussed above, but other assumptions come to mind, such as ‘self-similarity’ conditions employed in [5,13,22,27] for confidence intervals and bands.”
• Anti-concentration and honest, adaptive confidence bands (2013, unknown): “This condition is inspired by the path-breaking work of [20]; see also [36].”
• Uncertainty Quantification for the Horseshoe (with Discussion) (2016, unknown): “The preceding self-similarity condition plays the same role as the assumptions of “self-similarity” or “polished tail” used by [28, 16, 7, 26, 43, 41, 35] in their investigations of confidence sets in nonparametric density estimation and regression, or the “excessive-bias” restriction in [2] employe”
• CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, unknown): “The paper closest to the present one is Picard and Tribouley (2000) where pointwise adaptive confidence intervals are constructed in regression and Gaussian white noise.”
• Minimax or maxisets (2002, unknown): “Remark : The last inequality (28) states the equivalence of the Lq norm of f and Mr(f).”
• Adapting to Unknown Smoothness by Aggregation of Thresholded Wavelet Estimators (2006, unknown): “For further details about the density estimation via adaptive wavelet thresholded estimators, see [23], [19] and [47].”
• On adaptive inference and confidence bands (2011, unknown): “Giné and Nickl [12] recently suggested a new approach to this problem, partly inspired by Picard and Tribouley [28].”
• Confidence sets for nonparametric wavelet regression (2005, unknown): “The theorem also holds with a data-splitting scheme similar to that used in Nason (1996) and Picard and Tribouley (2000), where we use one half of the data to estimate the SURE-minimizing threshold and the other half to construct the confidence set.”
• An adaptation theory for nonparametric confidence intervals (2004, unknown): “Picard and Tribouley (2000) construct adaptive confidence intervals for functions at a point using a wavelet method which achieve optimal coverage accuracy up to a logarithmic factor although in this case the issue of optimal expected length is not addressed.”
• Adaptive estimation of a distribution function and its density in sup-norm loss by wavelet and spline projections (2008, unknown): “2 An Exponential inequality for the uniform deviations of the linear estimator To control the uniform deviations of the linear estimators from their means, one can use inequalities for the empirical process indexed by classes of functions F contained in K = { 2Kj(·, y) : y ∈ R, j ∈ N ∪ {0} } , (35) ”
• Free‐knot polynomial splines with confidence intervals (2003, unknown): “Wavelets are now alsowidely used and some recent literature has begun to investigate confidence intervals based on wavelet estimators (Picard and Tribouley, 2000).”