Abstract
We obtained a non-commutative Khinchine-type inequality under assumption that Rademacher random variables are dependent under condition that the sum of them is equal to some integer M.
References
[1] R. Bhatia, Matrix Analysis, Grad. Texts in Math. 169, Springer, New York, 1997. 10.1007/978-1-4612-0653-8Search in Google Scholar
[2] A. Buchholz, Operator Khintchine inequality in non-commutative probability, Math. Ann. 319 (2001), no. 1, 1–16. 10.1007/PL00004425Search in Google Scholar
[3] K. Burak and A. B. Kashlak, Nonparametric confidence regions via the analytic wild bootstrap, Canad. J. Statist. 51 (2023), 77–94. 10.1002/cjs.11687Search in Google Scholar
[4] S. Dirksen and E. Ricard, Some remarks on noncommutative Khintchine inequalities, Bull. Lond. Math. Soc. 45 (2013), no. 3, 618–624. 10.1112/blms/bds107Search in Google Scholar
[5] U. Haagerup and M. Musat, On the best constants in noncommutative Khintchine-type inequalities, J. Funct. Anal. 250 (2007), no. 2, 588–624. 10.1016/j.jfa.2007.05.014Search in Google Scholar
[6] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University, Cambridge, 1990. Search in Google Scholar
[7] A. B. Kashlak, Large scale permutation A/B testing for quantile differences, preprint (2022). Search in Google Scholar
[8] A. B. Kashlak, S. Myroshnychenko and S. Spektor, Analytic permutation testing for functional data ANOVA, J. Comput. Graph. Statist. (2022), 10.1080/10618600.2022.2069780. 10.1080/10618600.2022.2069780Search in Google Scholar
[9] A. B. Kashlak and W. Yuan, Computation-free nonparametric testing for local spatial association with application to the US and Canadian electorate, Spat. Stat. 48 (2022), Paper No. 100617. 10.1016/j.spasta.2022.100617Search in Google Scholar
[10]
F. Lust-Piquard,
Inégalités de Khintchine dans
[11] F. Lust-Piquard and G. Pisier, Noncommutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), no. 2, 241–260. 10.1007/BF02384340Search in Google Scholar
[12] G. Pisier, Introduction to Operator Space Theory, London Math. Soc. Lecture Note Ser. 294, Cambridge University, Cambridge, 2003. 10.1017/CBO9781107360235Search in Google Scholar
[13]
G. Pisier and E. Ricard,
The non-commutative Khintchine inequalities for
[14]
G. Pisier and Q. Xu,
Non-commutative
[15] S. Spektor, Restricted Khinchine inequality, Canad. Math. Bull. 59 (2016), no. 1, 204–210. 10.4153/CMB-2015-047-8Search in Google Scholar
[16] J. A. Tropp, On the conditioning of random subdictionaries, Appl. Comput. Harmon. Anal. 25 (2008), no. 1, 1–24. 10.1016/j.acha.2007.09.001Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
Articles in the same Issue
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order