Nonparametric Tests for Multivariate Association
Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent re...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/6/1112 |
| _version_ | 1797482100698382336 |
|---|---|
| author | Solomon W. Harrar Yan Xu |
| author_facet | Solomon W. Harrar Yan Xu |
| author_sort | Solomon W. Harrar |
| collection | DOAJ |
| description | Testing the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings. |
| first_indexed | 2024-03-09T22:23:30Z |
| format | Article |
| id | doaj.art-c951d4a99b4b4861a7c2d2b0c4b1206a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:23:30Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c951d4a99b4b4861a7c2d2b0c4b1206a2023-11-23T19:11:01ZengMDPI AGSymmetry2073-89942022-05-01146111210.3390/sym14061112Nonparametric Tests for Multivariate AssociationSolomon W. Harrar0Yan Xu1Dr. Bing Zhang Department of Statistics, College of Arts and Sciences, University of Kentucky, Lexington, KY 40506, USAMerck & Co., 351 North Sumneytown Pike, P.O. Box 1000, North Wales, PA 19454, USATesting the existence of association between a multivariate response and predictors is an important statistical problem. In this paper, we present nonparametric procedures that make no specific distributional, regression function, and covariance matrix assumptions. Our test is motivated by recent results in MANOVA tests for a large number of groups. Two types of tests are proposed. While it is natural to consider the classical approach for constructing the test by jointly considering all the variables together, we also investigate a composite test where variable-by-variable univariate tests are combined to form a multivariate test. The asymptotic distributions of the test statistics are derived in a unified manner by deriving the asymptotic matrix variate normal distribution of random matrices involved in the construction of the statistics. The tests have good numerical performance in finite samples. The application of the methods is illustrated with gene expression profiling of bronchial airway brushings.https://www.mdpi.com/2073-8994/14/6/1112multivariate datanonparametricMANOVAlack-of-fit testlarge number of groups |
| spellingShingle | Solomon W. Harrar Yan Xu Nonparametric Tests for Multivariate Association Symmetry multivariate data nonparametric MANOVA lack-of-fit test large number of groups |
| title | Nonparametric Tests for Multivariate Association |
| title_full | Nonparametric Tests for Multivariate Association |
| title_fullStr | Nonparametric Tests for Multivariate Association |
| title_full_unstemmed | Nonparametric Tests for Multivariate Association |
| title_short | Nonparametric Tests for Multivariate Association |
| title_sort | nonparametric tests for multivariate association |
| topic | multivariate data nonparametric MANOVA lack-of-fit test large number of groups |
| url | https://www.mdpi.com/2073-8994/14/6/1112 |
| work_keys_str_mv | AT solomonwharrar nonparametrictestsformultivariateassociation AT yanxu nonparametrictestsformultivariateassociation |