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On Khintchine type inequalities for $k$-wise independent Rademacher random variables
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pass, Brendan Spektor, Susanna |
| Copyright Year | 2017 |
| Abstract | We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ $k$-wise independent Rademacher random variables. We show that an analogue of Khintchine's inequality holds, with a constant $N^{1/2-k/2p}$, when $k$ is even. We then show that this result is sharp for $k=2$; in particular, a version of Khintchine's inequality for sequences of pairwise Rademacher variables \emph{cannot} hold with a constant independent of $N$. We also characterize the cases of equality and show that, although the vector achieving equality is not unique, it is unique (up to law) among the smaller class of exchangable vectors of pairwise independent Rademacher random variables. As a fortunate consequence of our work, we obtain similar results for $3$-wise independent vectors. |
| Starting Page | 35 |
| Ending Page | 39 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.spl.2017.09.002 |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1708.08775 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1708.08775v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.spl.2017.09.002 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
