IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v200y2023ics0167715223001025.html
   My bibliography  Save this article

Comparing weak and strong convergence of density functions

Author

Listed:
  • Walker, Stephen G.

Abstract

Weak convergence of a distribution does not imply the density converges with respect to the L1 metric. We prove that strong convergence can be established by showing that a smoothed and non-smoothed sequence of the densities converge to each other.

Suggested Citation

  • Walker, Stephen G., 2023. "Comparing weak and strong convergence of density functions," Statistics & Probability Letters, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:stapro:v:200:y:2023:i:c:s0167715223001025
    DOI: 10.1016/j.spl.2023.109878
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223001025
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109878?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. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265.
    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. Ryan Martin, 2021. "A Survey of Nonparametric Mixing Density Estimation via the Predictive Recursion Algorithm," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 97-121, May.
    2. De Blasi, Pierpaolo & Martínez, Asael Fabian & Mena, Ramsés H. & Prünster, Igor, 2020. "On the inferential implications of decreasing weight structures in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    3. Grazian, Clara & Villa, Cristiano & Liseo, Brunero, 2020. "On a loss-based prior for the number of components in mixture models," Statistics & Probability Letters, Elsevier, vol. 158(C).
    4. Qianwen Tan & Subhashis Ghosal, 2021. "Bayesian Analysis of Mixed-effect Regression Models Driven by Ordinary Differential Equations," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 3-29, May.
    5. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    6. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2023. "Forecasting with a panel Tobit model," Quantitative Economics, Econometric Society, vol. 14(1), pages 117-159, January.
    7. Li, Feng & Kang, Yanfei, 2018. "Improving forecasting performance using covariate-dependent copula models," International Journal of Forecasting, Elsevier, vol. 34(3), pages 456-476.
    8. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    9. Fisher, Mark & Jensen, Mark J., 2022. "Bayesian nonparametric learning of how skill is distributed across the mutual fund industry," Journal of Econometrics, Elsevier, vol. 230(1), pages 131-153.
    10. Cai, Jing-Heng & Song, Xin-Yuan & Lam, Kwok-Hap & Ip, Edward Hak-Sing, 2011. "A mixture of generalized latent variable models for mixed mode and heterogeneous data," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2889-2907, November.
    11. N. T. Longford & Pierpaolo D'Urso, 2011. "Mixture models with an improper component," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2511-2521, January.
    12. Ungolo, Francesco & Kleinow, Torsten & Macdonald, Angus S., 2020. "A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 68-84.
    13. Conti, Gabriella & Frühwirth-Schnatter, Sylvia & Heckman, James J. & Piatek, Rémi, 2014. "Bayesian exploratory factor analysis," Journal of Econometrics, Elsevier, vol. 183(1), pages 31-57.
    14. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    15. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    16. Park, Byung-Jung & Zhang, Yunlong & Lord, Dominique, 2010. "Bayesian mixture modeling approach to account for heterogeneity in speed data," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 662-673, June.
    17. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.
    18. Wu, C.C. & Lee, Jack C., 2007. "Estimation of a utility-based asset pricing model using normal mixture GARCH(1,1)," Economic Modelling, Elsevier, vol. 24(2), pages 329-349, March.
    19. Wang, Ketong & Porter, Michael D., 2018. "Optimal Bayesian clustering using non-negative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 395-411.
    20. Stefano Caria & Grant Gordon & Maximilian Kasy & Simon Quinn & Soha Shami & Alexander Teytelboym, 2020. "An Adaptive Targeted Field Experiment: Job Search Assistance for Refugees in Jordan," CESifo Working Paper Series 8535, CESifo.

    More about this item

    Keywords

    Kernel density; Modes; Smoothing;
    All these keywords.

    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:eee:stapro:v:200:y:2023:i:c:s0167715223001025. 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.