A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables

By D. L. Hanson, F. T. Wright. 1971

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

Generalized Results for the Existence and Consistency of the MLE in the Bradley-Terry-Luce Model (2021, methodology): “Using the Hanson-Wright inequality (Hanson & Wright, 1971) as in the proof of Theorem 1 of (Shah et al., 2016), we obtain that with probability at least 1 − e − t .”
Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method (2012, background): “bability. 12 DEANNA NEEDELL AND JOEL A. TROPP We do not have a reference for Proposition 3.7, but the result is probably not new. Appendix A offers a short proof based on the Hanson–Wright inequality [HW71] for Rademacher chaos. Let us pause to examine the hypothesis (3.1). Recall that, for a standa”
Estimates of moments and tails of Gaussian chaoses (2005, unknown): “For d= 1, we have Bα(x,W {x} d (α,4t)) = {y ∈R1 :α(x− y)≤ 4tEα(Gn1)} and (6) then follows by Lemma 1.”
Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2012, methodology): “At this point we will follow [19] and invoke a concentration estimate for quadratic forms essentially due to Hanson and Wright [29], [64].”
On the consistent separation of scale and variance for Gaussian random fields (2009, methodology): “The Hanson and Wright bound in [17] gives”
Hanson-Wright inequality and sub-gaussian concentration (2013, unknown): “28 72 v3 [ m at h. PR ] 1 O ct 2 01 3”
Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order (2013, methodology): “Such bounds for random quadratic forms in independent symmetric random variables with log-concave tails have been obtained by Latała [43] (the case of linear forms was solved earlier by Gluskin and Kwapień [29], whereas bounds for quadratic forms in Gaussian variables were obtained by Hanson-Wright”
Sub-Gaussian estimators of the mean of a random vector (2017, background): “…Σ , then the sample mean µ N is also multivariate normal with mean µ and covariance matrix (1 /N ) Σ and therefore, for δ ∈ (0 , 1), with probability at least 1 − δ , (cid:13)(cid:13)(cid:13) (cid:13)(cid:13)(cid:13) where λ max denotes the largest eigenvalue of Σ (see Hanson and Wright [7]).”
A note on the Hanson-Wright inequality for random vectors with dependencies (2014, background): “Our second result concerns a uniform version of the Hanson-Wright inequality for suprema of quadratic forms and is contained in the following Theorem 2.4.”
A modern maximum-likelihood theory for high-dimensional logistic regression (2018, methodology): “Applying the Hanson-Wright inequality [51,84] and the Sherman-Morrison-Woodbury formula (e.”
Robust dimension free isoperimetry in Gaussian space (2012, background): “9 from the result stated in [12], simply note that the operator norm is bounded by the Frobenius norm.”
Concentration inequalities for polynomials in α-sub-exponential random variables (2019, background): “Indeed, the Hanson–Wright inequality (see [14], [35], [29]) states that for a quadratic form in independent, centered sub-Gaussian random variables X1, .”
Universality of random matrices and local relaxation flow (2009, background): “Proposition C.2 (See [ 21 , 31]) Let bj , j = 1, 2 ,...,N be a sequence of real i.i.d.”