Titlebook: Concentration and Gaussian Approximation for Randomized Sums; Sergey Bobkov,Gennadiy Chistyakov,Friedrich G?tze Book 2023 The Editor(s) (i

cogitate

Proponent

https://doi.org/10.1007/978-1-4939-2602-2The aim is in particular to quantify the asymptotic normality of these distributions and to include dimensional refinements of such approximation in analogy with Edgeworth expansions (which however we consider up to order 2).

Blemish

向下

Time-Series Prediction and ApplicationsIn order to study deviations of the distribution functions . from the typical distribution . by means of the Kolmogorov distance, Berry–Esseen-type inequalities, which we discussed in Chapter 3, will be used. To this end we need to focus first on the behavior of characteristic functions of ..

種子

Amit Konar,Diptendu BhattacharyaIn order to deal with the main Problem 12.1.2, we start with the Kantorovich distance for bounding possible fluctuations of . around . on average.

誘惑

Moments and Correlation ConditionsThis definition is frequently used in Convex Geometry, especially for random vectors which are uniformly distributed over a convex body (in which case the body is called isotropic, cf. [144]).

parsimony

Standard Analytic ConditionsIn some problems/Sobolev-type inequalities, it makes sense to slightly modify the notion of the generalized modulus of gradient.

秘傳

Engulf

Sobolev-type InequalitiesAccording to the general equation (5.4), and since the geodesic and Euclidean distances are infinitesimally equivalent, the second order modulus of the gradient for functions . on the unit sphere is defined by

考古學(xué)

Linear Functionals on the SphereThe aim is in particular to quantify the asymptotic normality of these distributions and to include dimensional refinements of such approximation in analogy with Edgeworth expansions (which however we consider up to order 2).