An error bound in the Sudakov-Fernique inequality
By Sourav Chatterjee. 2005
53 citations recorded by the source corpus.
We obtain an asymptotically sharp error bound in the classical Sudakov-Fernique comparison inequality for finite collections of gaussian random variables. Our proof is short and self-contained, and gives an easy alternative argument for the classical inequality, extended to the case of non-centered processes.
Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability
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In Artificial Intelligence
- Victor Chernozhukov
- D. Chetverikov
- Kengo Kato
- Alexandre Belloni
- Yun Yang
- Anirban Bhattacharya
- Debdeep Pati
- Martin J. Wainwright
In Management Science and Operations Research
- Victor Chernozhukov
- Kengo Kato
- D. Chetverikov
- Yun Yang
- Anirban Bhattacharya
- Martin J. Wainwright
- Debdeep Pati
- David M. Blei
In Statistics and Probability
- Kengo Kato
- Victor Chernozhukov
- D. Chetverikov
- Alexandre Belloni
- Yun Yang
- Cun-Hui Zhang
- Christian Hansen
- Anirban Bhattacharya
Citations in the corpus
- Sharp thresholds for high-dimensional and noisy recovery of sparsity (2006, methodology): “If we set ∆ ∗ := max i,j S c | ∆ X ( i, j ) − ∆ Z ( i, j ) , then, by applying a known error bound for the Sudakov-Fernique inequality [5], we are guaranteed that We now show that the quantity ∆ ∗ is upper bounded by Using the inversion formula for block-partitioned matrices [22], we have In turn,…”
- Gaussian approximation of suprema of empirical processes (2012, background): “Consider, as in [6], the function Fβ : R p → R defined by”
- Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, background): “The result is derived in [30], and extends that of [23] who gave an explicit error in Sudakov-Fernique comparison of expecations of maxima of Gaussian random vectors.”
- Frequentist coverage and sup-norm convergence rate in Gaussian process regression (2017, background): “The comparison inequality extends the Sudakov–Fernique inequality for finite-dimensional Gaussians as stated in [12] to GPs. Theorem 3.4 (Gaussian process approximation of the centered posterior measure) .”
- Sparse Group Lasso: Consistency and Climate Applications (2012, unknown): “For ease of exposition, we assume the groups Gt are of the same size, say of m indices, so we have T groups of size m, and p = Tm.”