Nonparametric Goodness-of-Fit Testing Under Gaussian Models

By C. Pouet. 2004

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In Statistics and Probability

Citations in the corpus

Optimal inference in a class of regression models (2015, unknown): “PROOF: The result is immediate from results stated in Section 2.4.3 in Ingster and Suslina (2003), since the sets {Kf : f ∈ F̃} and {Kg : g ∈ G̃} are convex.”
Testing in mixed-effects FANOVA models (2006, methodology): “In addition, the above theorem demonstrates the degenerate behavior of the error probabilities of a which is also typical for adaptive testing (e.g., Ingster and Suslina, 2003).”
On adaptive inference and confidence bands (2011, background): “As we shall see in the proof of Theorem 2 below, an adaptive confidence band over P(ρn) can be used to test any such hypothesis consistently, and intuitively speaking an adaptive confidence band should thus only exist if ρn is of larger order than the minimax rate of testing between H0 and H1 in the”
Testing Many Moment Inequalities (2013, background): “ximately) α ∈ (0,1) for the former problem will lead to a conﬁdence region for the latter problem with coverage (approximately) at least 1−α (see Romano and Shaikh, 2See, for example, Ingster (1993); Ingster and Suslina (2003) for the minimax approach to hypothesis testing in nonparametric statistic”
Estimation and detection of functions from anisotropic Sobolev classes (2011, background): “1]); the second one, dealing with detection of a signal and obtained for the first time in a slightly different setup in Theorem 1 of [2], is a combination of statements from [6] (see [7, Sec.”
Hypothesis Testing for High-Dimensional Multinomials: A Selective Review (2017, methodology): “Classical work in hypothesis testing [Ingster and Suslina (2003), Ingster (1997)] has focused on characterizing the global minimax separation, that is, in understanding the quantity (2.2) εn = inf { ε : sup p0∈M R†n,ε(p0) ≤ 1/2 } , where M is defined in (2.1).”
Detection boundary in sparse regression (2010, background): “This question is closely related to the previous work by several authors on detection and classiﬁcation boundaries for the Gaussian sequence model [4, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24].”
Minimax optimality of permutation tests (2020, methodology): “We approach this problem from the minimax perspective pioneered by Ingster (1987), and further developed in subsequent works (Ingster and Suslina, 2003; Ingster, 1993; Baraud, 2002; Lepski and Spokoiny, 1999).”
Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates (2017, methodology): “Preliminaries: We begin by briefly introducing the lower bound technique due to Ingster (see for instance [14]).”
Adaptive confidence bands (2007, background): “The following lemma is essentially from Section 3.3 of Ingster and Suslina (2003).”