Title

On a multidimensional spherically invariant extension of the Rademacher-Gaussian comparison

Authors

Iosif Pinelis, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

9-19-2016

Abstract

It is shown that P(ǁa₁U₁+ · · · +a_nU_nǁ > u) ≤ cP(aǁZ_dǁ> u) for all real u, where U₁, : : : , U_n are independent random vectors uniformly distributed on the unit sphere in R^d, a₁, : : : , a_n are any real numbers, a := √(a²₁ + · · · · + a²_n ) ∕ d, Z_d is a standard normal random vector in R^d, and c = 2e³ ∕ 9 = 4.46 . . . .This constant factor is about 89 times as small as the one in a recent result by Nayar and Tkocz, who proved, by a different method, a corresponding conjecture by Oleszkiewicz. As an immediate application, a corresponding upper bound on the tail probabilities for the norm of the sum of arbitrary independent spherically invariant random vectors is given.

Publisher's Statement

© 2016 Project Euclid. Deposited in compliance with publisher policies. Publisher's version of record: http://dx.doi.org/10.1214/16-ECP23

Publication Title

Electronic Communications in Probability

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Pinelis, I. (2016). On a multidimensional spherically invariant extension of the Rademacher-Gaussian comparison. Electronic Communications in Probability, 21. http://doi.org/10.1214/16-ECP23
Retrieved from: https://digitalcommons.mtu.edu/math-fp/4

Version

Publisher's PDF