IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v64y2003i4p415-424.html
   My bibliography  Save this article

Nonparametric estimation of normal ranges given one-way ANOVA random effects assumptions

Author

Listed:
  • Hutson, Alan D.

Abstract

In this note, we compare three strategies that are commonly used in practice for estimating quantiles and quantile functions when data are assumed generated from a standard balanced one-way ANOVA random effects model, e.g. data from repeated assays, where the goal is to nonparametrically estimate/define a normal range. Strategy 1 consists of averaging the within subject values and then estimating quantiles based upon the averaged values in a standard fashion. Strategy 2 consists of estimating quantiles within each replication and then averaging the marginal quantiles over the replications. Strategy 3 consists of estimating quantiles and ignoring the repeated measures mechanism all together. We show that Strategy 1 is generally a poor choice when the goal is to refine the quantile estimation from a single replication through the application of repeated repetitions of an experiment. Strategy 2 and 3 are shown to be asymptotically equivalent.

Suggested Citation

  • Hutson, Alan D., 2003. "Nonparametric estimation of normal ranges given one-way ANOVA random effects assumptions," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 415-424, October.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:4:p:415-424
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00207-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
    2. Babu, G. Jogesh & Rao, C. Radhakrishna, 1988. "Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 15-23, 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. Averous, Jean & Meste, Michel, 1997. "Median Balls: An Extension of the Interquantile Intervals to Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 222-241, November.
    2. Hutson, Alan D., 2002. "Quasi-medians are robust and relatively efficient estimators of a common mean given multivariate normality," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 403-408, May.
    3. Barme-Delcroix, Marie-Francoise & Gather, Ursula, 2007. "Limit laws for multidimensional extremes," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1750-1755, December.
    4. Chitradipa Chakraborty & Subhra Sankar Dhar, 2020. "A Test for Multivariate Location Parameter in Elliptical Model Based on Forward Search Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 68-95, February.
    5. Dominicy, Yves & Hörmann, Siegfried & Ogata, Hiroaki & Veredas, David, 2013. "On sample marginal quantiles for stationary processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 28-36.
    6. Mohamed CHAOUCH & Ali GANNOUN & Jérôme SARACCO, 2008. "Conditional Spatial Quantile: Characterization and Nonparametric Estimation," Cahiers du GREThA (2007-2019) 2008-10, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    7. Nadja Klein & Thomas Kneib, 2020. "Directional bivariate quantiles: a robust approach based on the cumulative distribution function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 225-260, June.
    8. H. Barakat, 2001. "The Asymptotic Distribution Theory of Bivariate Order Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 487-497, September.
    9. Matthieu Garcin & Maxime L. D. Nicolas, 2021. "Nonparametric estimator of the tail dependence coefficient: balancing bias and variance," Papers 2111.11128, arXiv.org, revised Jul 2023.
    10. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    11. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01467857, HAL.
    12. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2018. "A novel multivariate risk measure: the Kendall VaR," Post-Print halshs-01467857, HAL.
    13. G. Jogesh Babu & Ashish Mahabal, 2016. "Skysurveys, Light Curves and Statistical Challenges," International Statistical Review, International Statistical Institute, vol. 84(3), pages 506-527, December.
    14. Yves Dominicy & Siegfried Hörmann & David Veredas & Hiroaki Ogata, 2012. "Marginal quantiles for stationary processes," Working Papers 1228, Banco de España.
    15. Baumeister, Marléne & Ditzhaus, Marc & Pauly, Markus, 2024. "Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    16. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    17. Matthieu Garcin & Dominique Guegan & Bertrand Hassani, 2017. "A novel multivariate risk measure: the Kendall VaR," Documents de travail du Centre d'Economie de la Sorbonne 17008r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2018.
    18. Sankar, Subhra & Bergsma, Wicher & Dassios, Angelos, 2017. "Testing independence of covariates and errors in nonparametric regression," LSE Research Online Documents on Economics 83780, London School of Economics and Political Science, LSE Library.
    19. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    20. Chung, EunYi & Romano, Joseph P., 2016. "Multivariate and multiple permutation tests," Journal of Econometrics, Elsevier, vol. 193(1), pages 76-91.

    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:64:y:2003:i:4:p:415-424. 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.