The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization
| dc.creator | Liu, Wei-Dong | |
| dc.creator | Lin, Zhengyan | |
| dc.creator | Shao, Qi-Man | |
| dc.date | 2009-01-16 | |
| dc.date.accessioned | 2026-07-07T12:31:04Z | |
| dc.date.available | 2026-07-07T12:31:04Z | |
| dc.description | Let $\mathbf{X}_1,...,\mathbf{X}_n$ be a random sample from a $p$-dimensional population distribution. Assume that $c_1n^α\leq p\leq c_2n^α$ for some positive constants $c_1,c_2$ and $α$. In this paper we introduce a new statistic for testing independence of the $p$-variates of the population and prove that the limiting distribution is the extreme distribution of type I with a rate of convergence $O((\log n)^{5/2}/\sqrt{n})$. This is much faster than $O(1/\log n)$, a typical convergence rate for this type of extreme distribution. A simulation study and application to stochastic optimization are discussed. | |
| dc.description | Published in at http://dx.doi.org/10.1214/08-AAP527 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/0901.2468 | |
| dc.identifier | http://arxiv.org/abs/0901.2468 | |
| dc.identifier | Annals of Applied Probability 2008, Vol. 18, No. 6, 2337-2366 | |
| dc.identifier | doi:10.1214/08-AAP527 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216329 | |
| dc.subject | Probability | |
| dc.subject | 60F05 (Primary) 62F05 (Secondary) | |
| dc.title | The asymptotic distribution and Berry--Esseen bound of a new test for independence in high dimension with an application to stochastic optimization | |
| dc.type | text |