Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC
The Hilbert--Schmidt Independence Criterion (HSIC) is a popular measure of the dependency between two random variables. The statistic dHSIC is an extension of HSIC that can be used to test joint independence of $d$ random variables. Such hypothesis testing for (joint) independence is often done usin...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Wiley
2021
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| _version_ | 1826294261154316288 |
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| author | Rindt, D Sejdinovic, D Steinsaltz, D |
| author_facet | Rindt, D Sejdinovic, D Steinsaltz, D |
| author_sort | Rindt, D |
| collection | OXFORD |
| description | The Hilbert--Schmidt Independence Criterion (HSIC) is a popular measure of
the dependency between two random variables. The statistic dHSIC is an
extension of HSIC that can be used to test joint independence of $d$ random
variables. Such hypothesis testing for (joint) independence is often done using
a permutation test, which compares the observed data with randomly permuted
datasets. The main contribution of this work is proving that the power of such
independence tests converges to 1 as the sample size converges to infinity.
This answers a question that was asked in (Pfister, 2018) Additionally this
work proves correct type 1 error rate of HSIC and dHSIC permutation tests and
provides guidance on how to select the number of permutations one uses in
practice. While correct type 1 error rate was already proved in (Pfister,
2018), we provide a modified proof following (Berrett, 2019), which extends to
the case of non-continuous data. The number of permutations to use was studied
e.g. by (Marozzi, 2004) but not in the context of HSIC and with a slight
difference in the estimate of the $p$-value and for permutations rather than
vectors of permutations. While the last two points have limited novelty we
include these to give a complete overview of permutation testing in the context
of HSIC and dHSIC. |
| first_indexed | 2024-03-07T03:42:54Z |
| format | Journal article |
| id | oxford-uuid:be81788c-12ed-495a-9942-e37f4034fc11 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:42:54Z |
| publishDate | 2021 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:be81788c-12ed-495a-9942-e37f4034fc112022-03-27T05:39:58ZConsistency of permutation test s of independence usingdistance covariance, HSIC and dHSICJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:be81788c-12ed-495a-9942-e37f4034fc11EnglishSymplectic ElementsWiley2021Rindt, DSejdinovic, DSteinsaltz, DThe Hilbert--Schmidt Independence Criterion (HSIC) is a popular measure of the dependency between two random variables. The statistic dHSIC is an extension of HSIC that can be used to test joint independence of $d$ random variables. Such hypothesis testing for (joint) independence is often done using a permutation test, which compares the observed data with randomly permuted datasets. The main contribution of this work is proving that the power of such independence tests converges to 1 as the sample size converges to infinity. This answers a question that was asked in (Pfister, 2018) Additionally this work proves correct type 1 error rate of HSIC and dHSIC permutation tests and provides guidance on how to select the number of permutations one uses in practice. While correct type 1 error rate was already proved in (Pfister, 2018), we provide a modified proof following (Berrett, 2019), which extends to the case of non-continuous data. The number of permutations to use was studied e.g. by (Marozzi, 2004) but not in the context of HSIC and with a slight difference in the estimate of the $p$-value and for permutations rather than vectors of permutations. While the last two points have limited novelty we include these to give a complete overview of permutation testing in the context of HSIC and dHSIC. |
| spellingShingle | Rindt, D Sejdinovic, D Steinsaltz, D Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title | Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title_full | Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title_fullStr | Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title_full_unstemmed | Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title_short | Consistency of permutation test s of independence usingdistance covariance, HSIC and dHSIC |
| title_sort | consistency of permutation test s of independence usingdistance covariance hsic and dhsic |
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