Test of independence for high-dimensional random vectors based on freeness in block correlation matrices
In this paper, we are concerned with the independence test for kk high-dimensional sub-vectors of a normal vector, with fixed positive integer kk. A natural high-dimensional extension of the classical sample correlation matrix, namely block correlation matrix, is proposed for this purpose. We then c...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2017
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| Online Access: | https://hdl.handle.net/10356/83955 http://hdl.handle.net/10220/42893 |
| _version_ | 1826118950988021760 |
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| author | Bao, Zhigang Hu, Jiang Pan, Guangming Zhou, Wang |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bao, Zhigang Hu, Jiang Pan, Guangming Zhou, Wang |
| author_sort | Bao, Zhigang |
| collection | NTU |
| description | In this paper, we are concerned with the independence test for kk high-dimensional sub-vectors of a normal vector, with fixed positive integer kk. A natural high-dimensional extension of the classical sample correlation matrix, namely block correlation matrix, is proposed for this purpose. We then construct the so-called Schott type statistic as our test statistic, which turns out to be a particular linear spectral statistic of the block correlation matrix. Interestingly, the limiting behavior of the Schott type statistic can be figured out with the aid of the Free Probability Theory and the Random Matrix Theory. Specifically, we will bring the so-called real second order freeness for Haar distributed orthogonal matrices, derived in Mingo and Popa (2013)[10], into the framework of this high-dimensional testing problem. Our test does not require the sample size to be larger than the total or any partial sum of the dimensions of the kk sub-vectors. Simulated results show the effect of the Schott type statistic, in contrast to those statistics proposed in Jiang and Yang (2013)[8] and Jiang, Bai and Zheng (2013)[7], is satisfactory. Real data analysis is also used to illustrate our method. |
| first_indexed | 2024-10-01T04:51:58Z |
| format | Journal Article |
| id | ntu-10356/83955 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:51:58Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | ntu-10356/839552023-02-28T19:39:36Z Test of independence for high-dimensional random vectors based on freeness in block correlation matrices Bao, Zhigang Hu, Jiang Pan, Guangming Zhou, Wang School of Physical and Mathematical Sciences Block correlation matrix Independence test In this paper, we are concerned with the independence test for kk high-dimensional sub-vectors of a normal vector, with fixed positive integer kk. A natural high-dimensional extension of the classical sample correlation matrix, namely block correlation matrix, is proposed for this purpose. We then construct the so-called Schott type statistic as our test statistic, which turns out to be a particular linear spectral statistic of the block correlation matrix. Interestingly, the limiting behavior of the Schott type statistic can be figured out with the aid of the Free Probability Theory and the Random Matrix Theory. Specifically, we will bring the so-called real second order freeness for Haar distributed orthogonal matrices, derived in Mingo and Popa (2013)[10], into the framework of this high-dimensional testing problem. Our test does not require the sample size to be larger than the total or any partial sum of the dimensions of the kk sub-vectors. Simulated results show the effect of the Schott type statistic, in contrast to those statistics proposed in Jiang and Yang (2013)[8] and Jiang, Bai and Zheng (2013)[7], is satisfactory. Real data analysis is also used to illustrate our method. MOE (Min. of Education, S’pore) Published version 2017-07-18T03:34:48Z 2019-12-06T15:35:18Z 2017-07-18T03:34:48Z 2019-12-06T15:35:18Z 2017 Journal Article Bao, Z., Hu, J., Pan, G., & Zhou, W. (2017). Test of independence for high-dimensional random vectors based on freeness in block correlation matrices. Electronic Journal of Statistics, 11(1), 1527-1548. https://hdl.handle.net/10356/83955 http://hdl.handle.net/10220/42893 10.1214/17-EJS1259 en Electronic Journal of Statistics © 2017 The author(s) (published by The Institute of Mathematical Statistics and The Bernoulli Society for Mathematical Statistics and Probability). This work is licensed under a Creative Commons Attribution 4.0 International License. 22 p. application/pdf |
| spellingShingle | Block correlation matrix Independence test Bao, Zhigang Hu, Jiang Pan, Guangming Zhou, Wang Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title | Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title_full | Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title_fullStr | Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title_full_unstemmed | Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title_short | Test of independence for high-dimensional random vectors based on freeness in block correlation matrices |
| title_sort | test of independence for high dimensional random vectors based on freeness in block correlation matrices |
| topic | Block correlation matrix Independence test |
| url | https://hdl.handle.net/10356/83955 http://hdl.handle.net/10220/42893 |
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