IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v63y2013icp148-159.html
   My bibliography  Save this article

Efficient estimation of the mode of continuous multivariate data

Author

Listed:
  • Hsu, Chih-Yuan
  • Wu, Tiee-Jian

Abstract

Mode estimation is an important task, because it has applications to data from a wide variety of sources. Many mode estimates have been proposed with most based on nonparametric density estimates. However, mode estimates obtained by such methods, although they perform excellently with large sample sizes, perform non-satisfactorily with practical (i.e., small to moderate) sample sizes. Recently, Bickel (2003) proposed an efficient method to estimate the mode of continuous univariate data, and showed that its performance is excellent with small to moderate sample sizes. In this paper, we extend Bickel’s method to continuous multivariate data by using the multivariate Box–Cox transform. The excellent performance of the proposed method at practical sample sizes is demonstrated by simulation examples and two real examples from the fields of climatology and image recognition.

Suggested Citation

  • Hsu, Chih-Yuan & Wu, Tiee-Jian, 2013. "Efficient estimation of the mode of continuous multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 148-159.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:148-159
    DOI: 10.1016/j.csda.2013.01.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313000339
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.01.018?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. A. Quintela-Del-Río & Ph. Vieu, 1997. "A nonparametric conditional mode estimate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 8(3), pages 253-266, September.
    2. Mokkadem, Abdelkader, 1988. "Mixing properties of ARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 29(2), pages 309-315, September.
    3. Junmei Jing & Inge Koch & Kanta Naito, 2012. "Polynomial Histograms for Multivariate Density and Mode Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 75-96, March.
    4. Th. Gasser & P. Hall & B. Presnell, 1998. "Nonparametric estimation of the mode of a distribution of random curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 681-691.
    5. S. Corti & F. Molteni & T. N. Palmer, 1999. "Signature of recent climate change in frequencies of natural atmospheric circulation regimes," Nature, Nature, vol. 398(6730), pages 799-802, April.
    6. Peter Hall, 2002. "Estimating and depicting the structure of a distribution of random functions," Biometrika, Biometrika Trust, vol. 89(1), pages 145-158, March.
    7. Bickel, David R. & Fruhwirth, Rudolf, 2006. "On a fast, robust estimator of the mode: Comparisons to other robust estimators with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3500-3530, August.
    8. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    9. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    10. Burman, Prabir & Polonik, Wolfgang, 2009. "Multivariate mode hunting: Data analytic tools with measures of significance," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1198-1218, July.
    11. Cheng, Ming-Yen & Hall, Peter, 1998. "On mode testing and empirical approximations to distributions," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 245-254, August.
    12. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
    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. Kirschstein, T. & Liebscher, S. & Porzio, G.C. & Ragozini, G., 2016. "Minimum volume peeling: A robust nonparametric estimator of the multivariate mode," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 456-468.
    2. Ruzankin, Pavel S. & Logachov, Artem V., 2020. "A fast mode estimator in multidimensional space," Statistics & Probability Letters, Elsevier, vol. 158(C).

    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. Merlevède, F. & Peligrad, M., 2016. "On the empirical spectral distribution for matrices with long memory and independent rows," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2734-2760.
    2. Huanchao Zhou & Zhidong Bai & Jiang Hu, 2023. "The Limiting Spectral Distribution of Large-Dimensional General Information-Plus-Noise-Type Matrices," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1203-1226, June.
    3. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
    4. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
    5. Kadiri Nadia & Rabhi Abbes & Bouchentouf Amina Angelika, 2018. "Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship," Dependence Modeling, De Gruyter, vol. 6(1), pages 197-227, November.
    6. Pavel Yaskov, 2018. "LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2032-2055, December.
    7. Couillet, Romain & Kammoun, Abla & Pascal, Frédéric, 2016. "Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 249-274.
    8. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
    9. Ningning Xia & Zhidong Bai, 2015. "Functional CLT of eigenvectors for large sample covariance matrices," Statistical Papers, Springer, vol. 56(1), pages 23-60, February.
    10. Jamshid Namdari & Debashis Paul & Lili Wang, 2021. "High-Dimensional Linear Models: A Random Matrix Perspective," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 645-695, August.
    11. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    12. Jean-Philippe Bouchaud & Laurent Laloux & M. Augusta Miceli & Marc Potters, 2005. "Large dimension forecasting models and random singular value spectra," Science & Finance (CFM) working paper archive 500066, Science & Finance, Capital Fund Management.
    13. Wang, Cheng & Yang, Jing & Miao, Baiqi & Cao, Longbing, 2013. "Identity tests for high dimensional data using RMT," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 128-137.
    14. Péché, S., 2006. "Non-white Wishart ensembles," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 874-894, April.
    15. Bai, Z.D. & Miao, Baiqi & Jin, Baisuo, 2007. "On limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 76-101, January.
    16. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
    17. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    18. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    19. Jerzy Rydlewski & Małgorzata Snarska & Dominik Mielczarek & Daniel Kosiorowski, 2014. "Sparse Methods for Analysis of Sparse Multivariate Data From Big Economic Databases," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(1), pages 111-132, January.
    20. Couillet, Romain & McKay, Matthew, 2014. "Large dimensional analysis and optimization of robust shrinkage covariance matrix estimators," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 99-120.

    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:63:y:2013:i:c:p:148-159. 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.