Web2.5 Maximal inequalities As we explained in the motivation for the definition of sub-Gaussian random variables, the definition implies that sub-Gaussian random variables … WebSudakov inequality on concentration of the maximum. Any use of this inequality will inevitably require controlling the expected maximum, which we do by way of Fernique’s …
Moving Beyond Sub-Gaussianity in High-Dimensional Statistics ...
Web12 apr. 2024 · We consider a random Hamiltonian H: Σ → R defined on a compact space Σ that admits a transitive action by a compact group G.When the law of H is G-invariant, we show its expected free energy relative to the unique G-invariant probability measure on Σ, which obeys a subadditivity property in the law of H itself. The bound is often tight for … Webgeometric mean inequality is a special case of an inequality for entropies of multivariate Gaussians. Theorem 3.2. For a continuous probability density function pon R with variance ˙2, h(p) 1 2 (1 + log(2ˇ˙2)); with equality if and only if pis Gaussian with variance ˙2, i.e., for some we have p(x) = (1= p 2ˇ˙)e (1=2)((x )=˙)2. kabeltyp unitronic fd cp 10x2x0.5
Maximal Inequality - an overview ScienceDirect Topics
Web1 dec. 2016 · Our coupling constructions are based on the Slepian–Stein methods and Gaussian comparison inequalities and built on the ideas in [3], [4], [5], [9], [6], [8], [7]. We emphasize that the construction of couplings in this paper is non-asymptotic, and so the class of functions F = F n may depend on n , and its complexity may grow as the sample … Web1 jul. 2008 · Basic statistics has its Chebyshev inequality, martingale theory has its maximal inequalities, Markov processes have large deviations, but all pale in … Web(Communicated by Tomasz Natkaniec) References [1] Abramowitz, M.—Stegun, I. A.: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, … kabel thermocouple