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Distribution-free tests of independence in high dimensions
- Source :
- Biometrika, Biometrika, vol 104, iss 4
- Publication Year :
- 2017
- Publisher :
- Oxford University Press, 2017.
-
Abstract
- We consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall's tau and Spearman's rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and propose tests that control the type I error in the high-dimensional setting where $d>n$. We further show that the two tests are rate-optimal in terms of power against sparse alternatives, and outperform competitors in simulations, especially when $d$ is large.<br />Comment: to appear in Biometrika
- Subjects :
- Statistics and Probability
Distribution free
Multivariate random variable
Statistics & Probability
General Mathematics
Kendall tau rank correlation coefficient
Linear rank statistic
Mathematics - Statistics Theory
Mutual independence
01 natural sciences
010104 statistics & probability
Gumbel distribution
Kendall’s tau
Spearman’s rho
Econometrics
0101 mathematics
Independence (probability theory)
Statistical hypothesis testing
Mathematics
Discrete mathematics
Numerical and Computational Mathematics
Rank-type U-statistic
Applied Mathematics
Statistics
010102 general mathematics
Articles
Agricultural and Biological Sciences (miscellaneous)
Statistics, Probability and Uncertainty
General Agricultural and Biological Sciences
Null hypothesis
Type I and type II errors
Subjects
Details
- Language :
- English
- ISSN :
- 14643510 and 00063444
- Volume :
- 104
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Biometrika
- Accession number :
- edsair.doi.dedup.....085fce77f1139490b57988c02a585099