IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i11p1089-1096.html
   My bibliography  Save this article

On the irregular behavior of LS estimators for asymptotically singular designs

Author

Listed:
  • Pázman, Andrej
  • Pronzato, Luc

Abstract

Optimum design theory sometimes yields singular designs. An example with a linear regression model often mentioned in the literature is used to illustrate the difficulties induced by such designs. The estimation of the model parameters [theta], or of a function of interest h([theta]), may be impossible with the singular design [xi]*. Depending on how [xi]* is approached by the empirical measure [xi]n of the design points, with n the number of observations, consistency is achieved but the speed of convergence may depend on [xi]n and on the value of [theta]. Even in situations where convergence is in and the asymptotic distribution of the estimator of [theta] or h([theta]) is normal, the asymptotic variance may still differ from that obtained from [xi]*.

Suggested Citation

  • Pázman, Andrej & Pronzato, Luc, 2006. "On the irregular behavior of LS estimators for asymptotically singular designs," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1089-1096, June.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:11:p:1089-1096
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00451-7
    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. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    2. Schwabe, Rainer, 1997. "Maximin efficient designs another view at D-optimality," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 109-114, September.
    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. Maryna Prus, 2019. "Optimal designs for minimax-criteria in random coefficient regression models," Statistical Papers, Springer, vol. 60(2), pages 465-478, April.
    2. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    3. Pal, Manisha & Mandal, Nripes Kumar, 2008. "Minimax designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 608-615, April.
    4. Luc Pronzato & Éric Thierry, 2002. "Sequential experimental design and response optimisation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 277-292, October.
    5. Dette, Holger & Melas, Viatcheslav B., 2008. "Optimal designs for estimating the slope of a regression," Technical Reports 2008,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Lorens Imhof & Weng Kee Wong, 2000. "A Graphical Method for Finding Maximin Efficiency Designs," Biometrics, The International Biometric Society, vol. 56(1), pages 113-117, March.
    7. Pal, Manisha & Mandal, Nripes K., 2006. "Optimum designs for optimum mixtures," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1369-1379, July.

    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:76:y:2006:i:11:p:1089-1096. 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.