Asymptotic distribution of the largest off-diagonal entry of correlation matrices

By Wang Zhou. 2007

70 citations recorded by the source corpus.

Suppose that we have observations from a -dimensional population. We are interested in testing that the variates of the population are independent under the situation where goes to infinity as . A test statistic is chosen to be , where is the sample correlation coefficient between the -th coordinate and the -th coordinate of the population. Under an independent hypothesis, we prove that the asymptotic distribution of is an extreme distribution of type , by using the Chen-Stein Poisson approximation method and the moderate deviations for sample correlation coefficients. As a statistically more relevant result, a limit distribution for , where is Spearman's rank correlation coefficient between the -th coordinate and the -th coordinate of the population, is derived

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9423abda36fc2b0e9586362b734b09b9a65ad2d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Fang Han
2. Zhao Ren
3. Mathias Drton
4. Tommaso Cai
5. Hongjian Shi
6. A. Hero
7. Bala Rajaratnam
8. Harrison H. Zhou

In Mathematical Physics

1. Mathias Drton
2. Bala Rajaratnam
3. A. Hero
4. Fan Yang
5. Tommaso Cai
6. Weidong Liu
7. Hongjian Shi
8. Fang Han

In Statistics and Probability

1. Tommaso Cai
2. Mathias Drton
3. Zhao Ren
4. Fang Han
5. Harrison H. Zhou
6. Weidong Liu
7. Hongjian Shi
8. A. Hero

Citations in the corpus

• Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “…test in Ledoit and Wolf (2002), Srivastava (2005), Birke and Dette (2005), and Chen et al. (2010), and maximum entrywise deviation test in Jiang (2004), Zhou (2007), Liu et al. (2008), Li et al. (2010), Li et al. (2012), Cai and Jiang (2011), Shao and Zhou (2014), and Cai, Liu, and Xia (2013).”
• Large-Scale Correlation Screening (2011, methodology): “Tests of diagonal covariance structure are often based on the maximum sample correlation coefficient, and has been mainly studied in the large p regime as n → ∞ (Jiang 2004; Li and Rosalsky 2006; Zhou 2007; Liu, Lin, and Shao 2008; Li, Liu, and Rosalsky 2009; Cai and Jiang 2011).”
• Testing mutual independence in high dimensions with sums of squares of rank correlations (2015, background): “He assumed higher-order moment conditions that were weakened in subsequent work (Li et al., 2010, 2012, Liu et al., 2008, Zhou, 2007).”
• High-dimensional consistent independence testing with maxima of rank correlations (2018, methodology): “Finally, Jiang (2004), Zhou (2007), and Han et al. (2017) proposed tests using the magnitude of the largest pairwise correlation statistics.”
• Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings (2013, unknown): “Further extensions and improvements are given in Zhou (2007), Liu, Lin, and Shao (2008), and Cai and Jiang (2011, 2012).”
• Testing independence in high dimensions with sums of rank correlations (2015, background): “He assumed higher-order moment conditions that were weakened in subsequent work [Zhou (2007), Liu, Lin and Shao (2008), Li, Liu and Rosalsky (2010), Li, Qi and Rosalsky (2012)].”
• THE ASYMPTOTIC DISTRIBUTION AND BERRY-ESSEEN BOUND OF A NEW TEST FOR INDEPENDENCE IN HIGH DIMENSION WITH AN APPLICATION TO STOCHASTIC OPTIMIZATION (2008, background): “Zhou [21] shows that the moment condition E|X1,1| < ∞ for some r > 30 can be weakened to x(6)P(|X1,1X1,2| ≥ x) → 0 as x →∞.”
• Likelihood Ratio Tests for High‐Dimensional Normal Distributions (2013, methodology): “For considering the construction of compressed sensing matrices, the statistical testing problems, the covariance structures of normal distributions, high dimensional regression in statistics and a wide range of applications including signal processing, medical imaging, and seismology, the largest o”