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math.PR2026
Effective-dimension bounds in the central limit theorem for centered Euclidean balls
Alexey Naumov, Sergey Samsonov, Vladimir Spokoiny +1
We establish a nonasymptotic Gaussian approximation bound over centered Euclidean balls for sums of independent, not necessarily identically distributed, random vectors in \(\mathb…
math.PR2023
Deviation bounds for the norm of a random vector under exponential moment conditions with applications
Vladimir Spokoiny
Hanson-Wright inequality provides a powerful tool for bounding the norm of a centered stochastic vector with sub-gaussian behavior. This paper extends the bounds to the c…
math.PR2023★ 1 cited
Concentration of a high dimensional sub-gaussian vector
Vladimir Spokoiny
This note describes the concentration phenomenon for a high dimensional sub-gaussian vector \( X \). In the Gaussian case, for any linear operator \( Q \), it holds \( P\bigl( \| Q…