IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v115y2013icp285-300.html
   My bibliography  Save this article

Weak conditions for shrinking multivariate nonparametric density estimators

Author

Listed:
  • Sancetta, Alessio

Abstract

Nonparametric density estimators on RK may fail to be consistent when the sample size n does not grow fast enough relative to reduction in smoothing. For example a Gaussian kernel estimator with bandwidths proportional to some sequence hn is not consistent if nhnK fails to diverge to infinity. The paper studies shrinkage estimators in this scenario and shows that we can still meaningfully use–in a sense to be specified in the paper–a nonparametric density estimator in high dimensions, even when it is not asymptotically consistent. Due to the “curse of dimensionality”, this framework is quite relevant to many practical problems. In this context, unlike other studies, the reason to shrink towards a possibly misspecified low dimensional parametric estimator is not to improve on the bias, but to reduce the estimation error.

Suggested Citation

  • Sancetta, Alessio, 2013. "Weak conditions for shrinking multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 285-300.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:285-300
    DOI: 10.1016/j.jmva.2012.09.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002230
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.09.009?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. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    3. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    4. Capistrán, Carlos & Timmermann, Allan, 2009. "Forecast Combination With Entry and Exit of Experts," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 428-440.
    5. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
    6. Sancetta, Alessio, 2008. "Sample covariance shrinkage for high dimensional dependent data," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 949-967, May.
    7. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    8. El Ghouch, Anouar & Genton, Marc G., 2009. "Local Polynomial Quantile Regression With Parametric Features," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1416-1429.
    9. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
    10. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    11. Marron, James Stephen & Härdle, Wolfgang, 1986. "Random approximations to some measures of accuracy in nonparametric curve estimation," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 91-113, October.
    Full references (including those not matched with items on IDEAS)

    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. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    2. Tae-Hwy Lee & Ekaterina Seregina, 2020. "Learning from Forecast Errors: A New Approach to Forecast Combination," Working Papers 202024, University of California at Riverside, Department of Economics.
    3. Fernandez-Perez, Adrian & Fuertes, Ana-Maria & Miffre, Joëlle, 2019. "A comprehensive appraisal of style-integration methods," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 134-150.
    4. Li, Jiahan & Chen, Weiye, 2014. "Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 996-1015.
    5. Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
    6. Dan Zhu & Qingwei Wang & John Goddard, 2022. "A new hedging hypothesis regarding prediction interval formation in stock price forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 697-717, July.
    7. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    8. Baumeister, Christiane & Kilian, Lutz & Lee, Thomas K., 2014. "Are there gains from pooling real-time oil price forecasts?," Energy Economics, Elsevier, vol. 46(S1), pages 33-43.
    9. Brave, Scott A. & Gascon, Charles & Kluender, William & Walstrum, Thomas, 2021. "Predicting benchmarked US state employment data in real time," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1261-1275.
    10. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    11. Fernando M. Duarte & Carlo Rosa, 2015. "The equity risk premium: a review of models," Economic Policy Review, Federal Reserve Bank of New York, issue 2, pages 39-57.
    12. Bartosz Uniejewski & Katarzyna Maciejowska, 2022. "LASSO Principal Component Averaging -- a fully automated approach for point forecast pooling," Papers 2207.04794, arXiv.org.
    13. Yi, Yongsheng & Ma, Feng & Zhang, Yaojie & Huang, Dengshi, 2019. "Forecasting stock returns with cycle-decomposed predictors," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 250-261.
    14. Lyócsa, Štefan & Molnár, Peter & Todorova, Neda, 2017. "Volatility forecasting of non-ferrous metal futures: Covariances, covariates or combinations?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 51(C), pages 228-247.
    15. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    16. Mauro Costantini & Ulrich Gunter & Robert M. Kunst, 2017. "Forecast Combinations in a DSGE‐VAR Lab," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(3), pages 305-324, April.
    17. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    18. Ferrara, Laurent & Marsilli, Clément & Ortega, Juan-Pablo, 2014. "Forecasting growth during the Great Recession: is financial volatility the missing ingredient?," Economic Modelling, Elsevier, vol. 36(C), pages 44-50.
    19. Paroissien, Emmanuel, 2020. "Forecasting bulk prices of Bordeaux wines using leading indicators," International Journal of Forecasting, Elsevier, vol. 36(2), pages 292-309.
    20. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.

    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:115:y:2013:i:c:p:285-300. 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.