skip to content

Faculty of Economics

Journal Cover

Klochkov, Y. and Zhivotovskiy, N.

Uniform Hanson-Wright Type Concentration Inequalities for Unbounded Entries via the Entropy Method

Electronic Journal of Probability

Vol. 25 pp. 1-30 (2020)

Abstract: This paper is devoted to uniform versions of the Hanson-Wright inequality for a random vector X ∈ Rn with independent subgaussian components. The core technique of the paper is based on the entropy method combined with truncations of both gradients of functions of interest and of the components of X itself. Our results recover, in particular, the classic uniform bound of Talagrand [28] for Rademacher chaoses and the more recent uniform result of Adamczak [2] which holds under certain rather strong assumptions on the distribution of X. We provide several applications of our techniques: we establish a version of the standard Hanson-Wright inequality, which is tighter in some regimes. Extending our results we show a version of the dimension-free matrix Bernstein inequality that holds for random matrices with a subexponential spectral norm. We apply the derived inequality to the problem of covariance estimation with missing observations and prove an almost optimal high probability version of the recent result of Lounici [21]. Finally, we show a uniform Hanson-Wright-type inequality in the Ising model under Dobrushin’s condition. A closely related question was posed by Marton [22].

Keywords: Concentration inequalities, matrix Bernstein inequality, modified logarithmic Sobolev inequalities, Rademacher chaos, uniform Hanson-Wright inequalities

Author links:

Publisher's Link:

Papers and Publications

Recent Publications

Porzio, T., Rossi, F. and Santangelo, G. The Human Side of Structural Transformation American Economic Review [2022]

Huffman, D., Raymond, C. and Shvets, J. Persistent Overconfidence and Biased Memory: Evidence from Managers American Economic Review [2022]

Rauh, C. and Valladares-Esteban, A. On the Black-White Gaps in Labor Supply and Earnings over the Lifecycle in the US Review of Economic Dynamics [2023]

Carneiro, P., Liu, K. and Salvanes, K. G. The Supply of Skill and Endogenous Technical Change: Evidence from a College Expansion Reform Journal of the European Economic Association [2023]