---
res:
bibo_abstract:
- Let Q = (Q1, . . . , Qn) be a random vector drawn from the uniform distribution
on the set of all n! permutations of {1, 2, . . . , n}. Let Z = (Z1, . . . , Zn),
where Zj is the mean zero variance one random variable obtained by centralizing
and normalizing Qj , j = 1, . . . , n. Assume that Xi , i = 1, . . . ,p are i.i.d.
copies of 1/√ p Z and X = Xp,n is the p × n random matrix with Xi as its ith row.
Then Sn = XX is called the p × n Spearman's rank correlation matrix which can
be regarded as a high dimensional extension of the classical nonparametric statistic
Spearman's rank correlation coefficient between two independent random variables.
In this paper, we establish a CLT for the linear spectral statistics of this nonparametric
random matrix model in the scenario of high dimension, namely, p = p(n) and p/n→c
∈ (0,∞) as n→∞.We propose a novel evaluation scheme to estimate the core quantity
in Anderson and Zeitouni's cumulant method in [Ann. Statist. 36 (2008) 2553-2576]
to bypass the so-called joint cumulant summability. In addition, we raise a two-step
comparison approach to obtain the explicit formulae for the mean and covariance
functions in the CLT. Relying on this CLT, we then construct a distribution-free
statistic to test complete independence for components of random vectors. Owing
to the nonparametric property, we can use this test on generally distributed random
variables including the heavy-tailed ones.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Zhigang
foaf_name: Bao, Zhigang
foaf_surname: Bao
foaf_workInfoHomepage: http://www.librecat.org/personId=442E6A6C-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-3036-1475
- foaf_Person:
foaf_givenName: Liang
foaf_name: Lin, Liang
foaf_surname: Lin
- foaf_Person:
foaf_givenName: Guangming
foaf_name: Pan, Guangming
foaf_surname: Pan
- foaf_Person:
foaf_givenName: Wang
foaf_name: Zhou, Wang
foaf_surname: Zhou
bibo_doi: 10.1214/15-AOS1353
bibo_issue: '6'
bibo_volume: 43
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: Institute of Mathematical Statistics@
dct_title: Spectral statistics of large dimensional spearman s rank correlation
matrix and its application@
...