Nonparametric Goodness-of-Fit Testing Under Gaussian Models

By Yu. I. Ingster, L. Suslina. 2002

295 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, methodology): “15 of Pg 69 of Ingster and Suslina [2003]. Its proof is given in Example 2.”
Minimax Testing of a Composite null Hypothesis Defined via a Quadratic Functional in the Model of regression (2012, methodology): “Those priors lead to the corresponding mixtures: × →{ } (cid:8) ) (cid:9) is the minimal total error probability for testing the simple null hypothesis H 0 : P = P π 1 n against the simple alternative H 1 : P = P π 2 n , then we have (see Proposition 2.11 in Ingster and Suslina (2003)) .”
Distribution-free Multiple Testing (2016, methodology): “Our inspiration for considering the normal (location) model comes from the seminal work of Ingster [18, 19] and [9] on testing the global null ⋂ i Hi.”
Inference on Causal and Structural Parameters using 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”
Impossible inference in econometrics: Theory and applications (2016, background): “Kraft (1955) targets the problem of testing any two sets of distributions and arrives at an important generalization of the theory of Bahadur and Savage (1956).”
Sketching as a Tool for Numerical Linear Algebra (2014, background): “n. Fact 8 ([117, p90]) dTV (µ,ν) ≤ p χ2(µ||ν). The next proposition gives a convenient upper boundon the χ2-divergence between a Gaussian distribution and a mixture of Gaussian distributions. Fact 9 ([65, p97]) χ2(N(0,In)∗µ||N(0,In)) ≤E[ehx,x ′i−1], where x,x′ ∼ µ are independent. We can now prove t”
Detection boundary in sparse regression (2010, methodology): “We will use the scheme of proving minimax lower bounds based on a reduction to the Bayes risk with the prior π, see for instance [21], Proposition 2.”
Minimax optimal conditional independence testing (2020, methodology): “Remarks: • In the case when `1 and `2 are constant, our lower bound on the critical radius εn(H0,H0,H1) ≥ c0n, scales as the familiar rate for goodness-of-fit testing in the nonparametric setting of εn n−2s/(4s+d) [2, 5, 19] (where in our setting we take d = 1 and s = 1, corresponding to the one-dim”