IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v135y2015icp71-88.html
   My bibliography  Save this article

Transformation-based nonparametric estimation of multivariate densities

Author

Listed:
  • Chang, Meng-Shiuh
  • Wu, Ximing

Abstract

We present a probability-integral-transformation-based estimator of multivariate densities. Given a sample of random vectors, we first transform the data into their corresponding marginal distributions. The marginal densities and the joint density of the transformed data are estimated nonparametrically. The joint density of the original data is constructed as the product of the density of the transformed data and marginal densities, which coincides with the copula representation of multivariate densities. We show that the Kullback–Leibler Information Criterion (KLIC) between the true density and its estimate can be decomposed into the KLIC of the marginal densities and that of the copula density. We derive the convergence rate of the proposed estimator in terms of the KLIC and propose a supervised hierarchical procedure of model selection. Monte Carlo simulations demonstrate the good performance of the estimator. An empirical example on the US and UK stock markets is presented. The estimated conditional copula density provides useful insight into the joint movements of the US and UK markets under extreme Asian markets.

Suggested Citation

  • Chang, Meng-Shiuh & Wu, Ximing, 2015. "Transformation-based nonparametric estimation of multivariate densities," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 71-88.
    • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:71-88
    DOI: 10.1016/j.jmva.2014.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002656
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.11.010?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. Aurore Delaigle & Peter Hall & Jiashun Jin, 2011. "Robustness and accuracy of methods for high dimensional data analysis based on Student's t‐statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 283-301, June.
    2. Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
    3. Cadima, Jorge & Cerdeira, J. Orestes & Minhoto, Manuel, 2004. "Computational aspects of algorithms for variable selection in the context of principal components," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 225-236, September.
    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. Perloff, Jeffrey M. & Schlenker, Wolfram & Sears, Molly & Wu, Ximing, 2020. "Crop Failures from Temperature and Precipitation Shocks: Implications for U.S. Crop Insurance," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304540, Agricultural and Applied Economics Association.
    2. Nan Yang & Yu Huang & Dengxu Hou & Songkai Liu & Di Ye & Bangtian Dong & Youping Fan, 2019. "Adaptive Nonparametric Kernel Density Estimation Approach for Joint Probability Density Function Modeling of Multiple Wind Farms," Energies, MDPI, vol. 12(7), pages 1-15, April.

    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. Colosimo Bianca Maria & Moya Ester Gutierrez & Moroni Giovanni & Petrò Stefano, 2008. "Statistical Sampling Strategies for Geometric Tolerance Inspection by CMM," Stochastics and Quality Control, De Gruyter, vol. 23(1), pages 109-121, January.
    2. Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    3. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    4. Pacheco, Joaquín & Casado, Silvia & Porras, Santiago, 2013. "Exact methods for variable selection in principal component analysis: Guide functions and pre-selection," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 95-111.
    5. Ronaldo Dias & Nancy L. Garcia & Guilherme Ludwig & Marley A. Saraiva, 2015. "Aggregated functional data model for near-infrared spectroscopy calibration and prediction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 127-143, January.
    6. Dennis Dobler & Markus Pauly, 2018. "Bootstrap- and permutation-based inference for the Mann–Whitney effect for right-censored and tied data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 639-658, September.
    7. Brosnan, Kylie & Grün, Bettina & Dolnicar, Sara, 2018. "Identifying superfluous survey items," Journal of Retailing and Consumer Services, Elsevier, vol. 43(C), pages 39-45.
    8. Cribari-Neto, Francisco, 1993. "The Cyclical Component in Brazilian GDP," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 13(1), April.
    9. Lopes, Hedibert F. & Dias, Ronaldo, 2011. "Bayesian mixture of parametric and nonparametric density estimation: A Misspecification Problem," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 31(1), March.
    10. J. S. Marron & S. S. Chung, 2001. "Presentation of smoothers: the family approach," Computational Statistics, Springer, vol. 16(1), pages 195-207, March.
    11. Fouskakis, D., 2012. "Bayesian variable selection in generalized linear models using a combination of stochastic optimization methods," European Journal of Operational Research, Elsevier, vol. 220(2), pages 414-422.
    12. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    13. Vincent J. Carey & Carol J. Baker & Richard Platt, 2001. "Bayesian Inference on Protective Antibody Levels Using Case‐Control Data," Biometrics, The International Biometric Society, vol. 57(1), pages 135-142, March.
    14. Kapetanios, George, 2007. "Variable selection in regression models using nonstandard optimisation of information criteria," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 4-15, September.
    15. Huh, Jib & Park, Cheolwoo, 2015. "Theoretical investigation of an exploratory approach for log-density in scale-space," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 272-279.
    16. Teruko Takada, 2001. "Nonparametric density estimation: A comparative study," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-10.
    17. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
    18. A. Pedro Duarte Silva, 2009. "Exact and heuristic algorithms for variable selection: Extended Leaps and Bounds," Working Papers de Economia (Economics Working Papers) 01, Católica Porto Business School, Universidade Católica Portuguesa.
    19. Talamakrouni, Majda & Van Keilegom, Ingrid & El Ghouch, Anouar, 2016. "Parametrically guided nonparametric density and hazard estimation with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 308-323.
    20. Tomas Ruzgas & Mantas Lukauskas & Gedmantas Čepkauskas, 2021. "Nonparametric Multivariate Density Estimation: Case Study of Cauchy Mixture Model," Mathematics, MDPI, vol. 9(21), pages 1-22, October.

    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:jmvana:v:135:y:2015:i:c:p:71-88. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.