Confidence balls in Gaussian regression

By Y. Baraud. 2004

63 citations recorded by the source corpus.

Starting from the observation of an R^n-Gaussian vector of mean f and covariance matrix \\sigma^2 I_n (I_n is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5fa66112ee3821b4968cdd265a7f68b1da835bfb

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In Artificial Intelligence

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Citations in the corpus

Confidence sets in sparse regression (2012, unknown): “A first attempt to construct such a confidence set, inspired by Li (1989), Beran and Dümbgen (1998), Baraud (2004) in nonparametric regression problems, is based on estimating the accuracy of estimation in (2) directly via sample splitting.”
Adaptive confidence bands (2007, background): “L2 confidence sets have been studied by Li (1999), Juditsky and Lambert-Lacroix (2002), Beran and Dümbgen (1998), Genovese and Wasserman (2004), Baraud (2004), Hoffman and Lepski (2003), Cai and Low (2004), and Robins and van der Vaart (2004).”
Adaptive confidence sets in $$L^2$$ (2011, background): “We note first that for s ≤ 2r adaptive confidence sets exist without any additional restrictions—this is a main finding of the papers [6,21,28] and has important precursors in [1,16,24].”
Adaptive Confidence Balls (2006, background): “Baraud [1] is a further development of both Li [11] and Hoffman and Lepski [9] concentrating on confidence balls which perform well over a finite family of linear subspaces.”
On adaptive inference and confidence bands (2011, background): “It was already noted or implicitly used in [1, 5, 15, 19, 29] that there is a generic connection between adaptive confidence sets and minimax distinguishability of certain nonparametric hypotheses.”
CONFIDENCE BANDS IN DENSITY ESTIMATION (2010, methodology): “34) N3(t)v +N3(t+1)v ((1))+N3(t+2)v (2) = λN3(s)v +λN3(s+1)v +λN3(s+2)v .”
On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection (2006, background): “Breiman (1992) called this situation “a quiet scandal in the statistical community.”
Simultaneous confidence bands for nonparametric regression with functional data (2009, methodology): “We also point to Baraud (2004) for the computation of SCI on an increasing number of (fixed) design points, and to Deheuvels and Mason (2004) for SCB with asymptotic coverage level 100%.”