Abstract
There has been an increasing interest in testing the equality of large Pearson’s correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson’s case, testing the equality of large rank-based statistics has not been well explored and requires us to develop new methods and theory. In this paper, we provide a framework for testing the equality of two large U-statistic based correlation matrices, which include the rank-based correlation matrices as special cases. Our approach exploits extreme value statistics and the Jackknife estimator for uncertainty assessment and is valid under a fully nonparametric model. Theoretically, we develop a theory for testing the equality of U-statistic based correlation matrices. We then apply this theory to study the problem of testing large Kendall’s tau correlation matrices and demonstrate its optimality. For proving this optimality, a novel construction of least favorable distributions is developed for the correlation matrix comparison.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1472-1503 |
| Number of pages | 32 |
| Journal | Bernoulli |
| Volume | 25 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 1 2019 |
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Keywords
- Extreme value type I distribution
- Hypothesis testing
- Jackknife variance estimator
- Kendall’s tau
- U-statistics
ASJC Scopus subject areas
- Statistics and Probability
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An extreme-value approach for testing the equality of large U-statistic based correlation matrices. / Zhou, Cheng; Han, Fang; Zhang, Xin Sheng; Liu, Han.
In: Bernoulli, Vol. 25, No. 2, 01.05.2019, p. 1472-1503.Research output: Contribution to journal › Article
TY - JOUR
T1 - An extreme-value approach for testing the equality of large U-statistic based correlation matrices
AU - Zhou, Cheng
AU - Han, Fang
AU - Zhang, Xin Sheng
AU - Liu, Han
PY - 2019/5/1
Y1 - 2019/5/1
N2 - There has been an increasing interest in testing the equality of large Pearson’s correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson’s case, testing the equality of large rank-based statistics has not been well explored and requires us to develop new methods and theory. In this paper, we provide a framework for testing the equality of two large U-statistic based correlation matrices, which include the rank-based correlation matrices as special cases. Our approach exploits extreme value statistics and the Jackknife estimator for uncertainty assessment and is valid under a fully nonparametric model. Theoretically, we develop a theory for testing the equality of U-statistic based correlation matrices. We then apply this theory to study the problem of testing large Kendall’s tau correlation matrices and demonstrate its optimality. For proving this optimality, a novel construction of least favorable distributions is developed for the correlation matrix comparison.
AB - There has been an increasing interest in testing the equality of large Pearson’s correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson’s case, testing the equality of large rank-based statistics has not been well explored and requires us to develop new methods and theory. In this paper, we provide a framework for testing the equality of two large U-statistic based correlation matrices, which include the rank-based correlation matrices as special cases. Our approach exploits extreme value statistics and the Jackknife estimator for uncertainty assessment and is valid under a fully nonparametric model. Theoretically, we develop a theory for testing the equality of U-statistic based correlation matrices. We then apply this theory to study the problem of testing large Kendall’s tau correlation matrices and demonstrate its optimality. For proving this optimality, a novel construction of least favorable distributions is developed for the correlation matrix comparison.
KW - Extreme value type I distribution
KW - Hypothesis testing
KW - Jackknife variance estimator
KW - Kendall’s tau
KW - U-statistics
UR - http://www.scopus.com/inward/record.url?scp=85064054301&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85064054301&partnerID=8YFLogxK
U2 - 10.3150/18-BEJ1027
DO - 10.3150/18-BEJ1027
M3 - Article
AN - SCOPUS:85064054301
VL - 25
SP - 1472
EP - 1503
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 2
ER -