IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v148y2020ics0167947320300463.html
   My bibliography  Save this article

A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection

Author

Listed:
  • Najarzadeh, Dariush

Abstract

The multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and a set of covariates. Testing the hypothesis of zero MCC has always been important in multiple correlation analysis. For testing this hypothesis, due to the singularity of the sample covariance matrix in high-dimensional data, the classical testing procedures are no longer usable. To test the null hypothesis of zero MCC in high-dimensional normal data, a simple testing procedure is proposed by using the random projection and union-intersection methodologies. Some simulations are carried out to verify the performance evaluation of the proposed test. The results are found to be very convincing. In the end, the experimental validation of the proposed test is carried out on mice tumor data.

Suggested Citation

  • Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:csdana:v:148:y:2020:i:c:s0167947320300463
    DOI: 10.1016/j.csda.2020.106955
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320300463
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.106955?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shurong Zheng & Dandan Jiang & Zhidong Bai & Xuming He, 2014. "Inference on multiple correlation coefficients with moderately high dimensional data," Biometrika, Biometrika Trust, vol. 101(3), pages 748-754.
    2. Ding, Cherng G., 1996. "On the computation of the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 345-350, August.
    3. Benton, Denise & Krishnamoorthy, K., 2003. "Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 249-267, June.
    4. Gupta, Somesh Das, 1977. "Tests on multiple correlation coefficient and multiple partial correlation coefficient," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 82-88, March.
    5. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    6. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    7. Tan, Ming & Fang, Hong-Bin & Tian, Guo-Liang & Wei, Gang, 2005. "Testing multivariate normality in incomplete data of small sample size," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 164-179, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Somayeh Abusaleh & Dariush Najarzadeh, 2024. "Simple tests on multiple correlation coefficient in high-dimensional normal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(5), pages 1381-1401, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ali Baharev & Hermann Schichl & Endre Rév, 2017. "Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy," Computational Statistics, Springer, vol. 32(2), pages 763-779, June.
    2. Matsushita, Yukitoshi & Otsu, Taisuke, 2020. "Jackknife empirical likelihood: small bandwidth, sparse network and high-dimension asymptotic," LSE Research Online Documents on Economics 106488, London School of Economics and Political Science, LSE Library.
    3. Ogasawara, Haruhiko, 2016. "Bias correction of the Akaike information criterion in factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 144-159.
    4. Kyriakopoulou, Dimitra & Demos, Antonis, 2010. "Edgeworth and Moment Approximations: The Case of MM and QML Estimators for the MA (1) Models," MPRA Paper 122393, University Library of Munich, Germany.
    5. Izabela Oliveira & Daniel Ferreira, 2013. "Computing the noncentral gamma distribution, its inverse and the noncentrality parameter," Computational Statistics, Springer, vol. 28(4), pages 1663-1680, August.
    6. Tomasz Burzykowski & Geert Molenberghs & Marc Buyse, 2004. "The validation of surrogate end points by using data from randomized clinical trials: a case‐study in advanced colorectal cancer," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(1), pages 103-124, February.
    7. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    8. Dias, José Carlos & Vidal Nunes, João Pedro, 2018. "Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral χ2 random variable," European Journal of Operational Research, Elsevier, vol. 265(2), pages 559-570.
    9. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    10. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    11. Ogasawara, Haruhiko, 2009. "On the estimators of model-based and maximal reliability," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1232-1244, July.
    12. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
    13. Peter M. Robinson & Francesca Rossi, 2014. "Improved Lagrange multiplier tests in spatial autoregressions," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 139-164, February.
    14. Alex N Nguyen Ba & Bob Strome & Jun Jie Hua & Jonathan Desmond & Isabelle Gagnon-Arsenault & Eric L Weiss & Christian R Landry & Alan M Moses, 2014. "Detecting Functional Divergence after Gene Duplication through Evolutionary Changes in Posttranslational Regulatory Sequences," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-15, December.
    15. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    16. Bruno Ebner & Norbert Henze, 2020. "Tests for multivariate normality—a critical review with emphasis on weighted $$L^2$$ L 2 -statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 845-892, December.
    17. Nina Ilysheva & Elena Baldesku & Ulugbek Zakirov, 2017. "Detection of the Interdependence of Economic Development and Environmental Performance at the Industry Level," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 13(4), pages 19-29.
    18. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    19. Carlos Miguel Glória & José Carlos Dias & Aricson Cruz, 2024. "Pricing levered warrants under the CEV diffusion model," Review of Derivatives Research, Springer, vol. 27(1), pages 55-84, April.
    20. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:148:y:2020:i:c:s0167947320300463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.