IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v87y2019i3p1055-1069.html
   My bibliography  Save this article

Power in High‐Dimensional Testing Problems

Author

Listed:
  • Anders Bredahl Kock
  • David Preinerstorfer

Abstract

Fan, Liao, and Yao (2015) recently introduced a remarkable method for increasing the asymptotic power of tests in high‐dimensional testing problems. If applicable to a given test, their power enhancement principle leads to an improved test that has the same asymptotic size, has uniformly non‐inferior asymptotic power, and is consistent against a strictly broader range of alternatives than the initially given test. We study under which conditions this method can be applied and show the following: In asymptotic regimes where the dimensionality of the parameter space is fixed as sample size increases, there often exist tests that cannot be further improved with the power enhancement principle. However, when the dimensionality of the parameter space increases sufficiently slowly with sample size and a marginal local asymptotic normality (LAN) condition is satisfied, every test with asymptotic size smaller than 1 can be improved with the power enhancement principle. While the marginal LAN condition alone does not allow one to extend the latter statement to all rates at which the dimensionality increases with sample size, we give sufficient conditions under which this is the case.

Suggested Citation

  • Anders Bredahl Kock & David Preinerstorfer, 2019. "Power in High‐Dimensional Testing Problems," Econometrica, Econometric Society, vol. 87(3), pages 1055-1069, May.
    • Handle: RePEc:wly:emetrp:v:87:y:2019:i:3:p:1055-1069
    DOI: 10.3982/ECTA15844
    as

    Download full text from publisher

    File URL: https://doi.org/10.3982/ECTA15844
    Download Restriction: no
    File URL: https://libkey.io/10.3982/ECTA15844?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Swensen, Anders Rygh, 1985. "The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 54-70, February.
    2. Zhong, Ping-Shou & Chen, Song Xi, 2011. "Tests for High-Dimensional Regression Coefficients With Factorial Designs," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 260-274.
    3. Pinelis, Iosif, 2014. "Schur2-concavity properties of Gaussian measures, with applications to hypotheses testing," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 384-397.
    4. Bernard Garel & Marc Hallin, 1995. "Local asymptotic normality of multivariate ARMA processes with a linear trend," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 551-579, September.
    5. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2012. "Signal Detection in High Dmension: The Multispiked Case," Working Papers ECARES ECARES 2012-036, ULB -- Universite Libre de Bruxelles.
    6. Alexei Onatski & Marcelo Moreira J. & Marc Hallin, 2011. "Asymptotic Power of Sphericity Tests for High-Dimensional Data," Working Papers ECARES ECARES 2011-018, ULB -- Universite Libre de Bruxelles.
    7. Chen, Song Xi & Li, Jun & Zhong, Pingshou, 2014. "Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation," MPRA Paper 59815, University Library of Munich, Germany.
    8. Ley, Christophe & Paindaveine, Davy & Verdebout, Thomas, 2015. "High-dimensional tests for spherical location and spiked covariance," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 79-91.
    9. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
    10. T. Tony Cai & Weidong Liu & Yin Xia, 2014. "Two-sample test of high dimensional means under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 349-372, March.
    11. Pupashenko, Daria & Ruckdeschel, Peter & Kohl, Matthias, 2015. "L2 differentiability of generalized linear models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 155-164.
    12. Christine Cutting & Davy Paindaveine & Thomas Verdebout, 2015. "Testing Uniformity on High-Dimensional Spheres against Contiguous Rotationally Symmetric Alternatives," Working Papers ECARES ECARES 2015-04, ULB -- Universite Libre de Bruxelles.
    13. Marc Hallin & Masanobu Taniguchi & Abdeslam Serroukh & Kokyo Choy, 1999. "Local asymptotic normality for regression models with long-memory disturbance, with statistical applications," ULB Institutional Repository 2013/2091, ULB -- Universite Libre de Bruxelles.
    14. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
    15. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
    16. Srivastava, Muni S. & Katayama, Shota & Kano, Yutaka, 2013. "A two sample test in high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 349-358.
    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. Anders Bredahl Kock & David Preinerstorfer, 2021. "Superconsistency of Tests in High Dimensions," Papers 2106.03700, arXiv.org, revised Jan 2022.
    2. Ge, S. & Li, S. & Linton, O., 2020. "A Dynamic Network of Arbitrage Characteristics," Cambridge Working Papers in Economics 2060, Faculty of Economics, University of Cambridge.
    3. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.
    4. David Preinerstorfer, 2018. "How to avoid the zero-power trap in testing for correlation," Papers 1812.10752, arXiv.org.
    5. He, Yi & Jaidee, Sombut & Gao, Jiti, 2023. "Most powerful test against a sequence of high dimensional local alternatives," Journal of Econometrics, Elsevier, vol. 234(1), pages 151-177.
    6. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.

    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. Zhang, Jin-Ting & Guo, Jia & Zhou, Bu, 2017. "Linear hypothesis testing in high-dimensional one-way MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 200-216.
    2. Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    3. Ayyala, Deepak Nag & Park, Junyong & Roy, Anindya, 2017. "Mean vector testing for high-dimensional dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 136-155.
    4. Ma, Yingying & Lan, Wei & Wang, Hansheng, 2015. "A high dimensional two-sample test under a low dimensional factor structure," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 162-170.
    5. Feng, Long & Sun, Fasheng, 2015. "A note on high-dimensional two-sample test," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 29-36.
    6. Zhang, Jie & Pan, Meng, 2016. "A high-dimension two-sample test for the mean using cluster subspaces," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 87-97.
    7. Shen, Yanfeng & Lin, Zhengyan, 2015. "An adaptive test for the mean vector in large-p-small-n problems," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 25-38.
    8. Francq, Christian & Zakoian, Jean-Michel, 2023. "Local Asymptotic Normality Of General Conditionally Heteroskedastic And Score-Driven Time-Series Models," Econometric Theory, Cambridge University Press, vol. 39(5), pages 1067-1092, October.
    9. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
    10. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.
    11. Hyodo, Masashi & Watanabe, Hiroki & Seo, Takashi, 2018. "On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 160-173.
    12. Yuanyuan Jiang & Xingzhong Xu, 2022. "A Two-Sample Test of High Dimensional Means Based on Posterior Bayes Factor," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    13. Davy Paindaveine & Thomas Verdebout, 2013. "Universal Asymptotics for High-Dimensional Sign Tests," Working Papers ECARES ECARES 2013-40, ULB -- Universite Libre de Bruxelles.
    14. Ghosh, Santu & Ayyala, Deepak Nag & Hellebuyck, Rafael, 2021. "Two-sample high dimensional mean test based on prepivots," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    15. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    16. Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
    17. He, Yong & Zhang, Mingjuan & Zhang, Xinsheng & Zhou, Wang, 2020. "High-dimensional two-sample mean vectors test and support recovery with factor adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    18. Christine Cutting & Davy Paindaveine & Thomas Verdebout, 2015. "Testing Uniformity on High-Dimensional Spheres against Contiguous Rotationally Symmetric Alternatives," Working Papers ECARES ECARES 2015-04, ULB -- Universite Libre de Bruxelles.
    19. Wang, Wei & Lin, Nan & Tang, Xiang, 2019. "Robust two-sample test of high-dimensional mean vectors under dependence," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 312-329.
    20. Zhang, Huaiyu & Wang, Haiyan, 2021. "A more powerful test of equality of high-dimensional two-sample means," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

    Statistics

    Access and download statistics

    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:wly:emetrp:v:87:y:2019:i:3:p:1055-1069. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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.