Advanced Search
MyIDEAS: Login to save this article or follow this journal

Combining Estimates of Tectonic Plate Rotations:, : An Extension of Welch's Method to Spherical Regression

Contents:

Author Info

  • Kirkwood, Bessie H.
  • Chang, Ted
Registered author(s):

    Abstract

    The relative motion between two diverging tectonic plates is a rotation of the sphere. Given measurements of points on the boundaries of the plates, the rotation can be estimated by minimizing a function which is asymptotically (as the concentration parameter of the data distribution goes to infinity) the sum of squared residuals of a linear regression. The linear approximation permits construction of an asymptotic confidence region for the rotation. To estimate the relative motion between plates that converge, it is necessary to combine two or more rotations of diverging plates, and previous methods required the assumption that separate data sets for all of the rotation estimates have the same concentration parameter. This assumption is frequently contradicted by data, indicating heteroscedasticity in the linear regression model. One successful approach to the problem in the linear model due to Welch, involves sample size asymptotics. A similar solution in the non- linear model thus depends on two kinds of asymptotics. We examine two types of general spherical regression models where the parameter estimate is obtained by maximizing or minimizing a particular function. We establish conditions under which the function converges to a residual sum of squares of linear regression as both concentration parameter and sample size go to infinity. Applying the double-convergence asymptotics to tectonic plate data yields asymptotic confidence regions for combined rotation estimates. The confidence region constructions we propose are appropriate for small to moderate sample sizes. Two kinds of confidence regions are constructed, one of which uses all the data for the separate rotation estimates; the other is a conservative approximation of the first, using only summary statistics from the separate estimates. Simulation runs indicate that both of the new constructions produce confidence regions much more consistent with nominal size, particularly when sample sizes are very different and concentration parameters of the data sets are very unequal.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://www.sciencedirect.com/science/article/B6WK9-45J4Y1D-14/2/005816d0f38d7c236890c1e624a40be6
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 65 (1998)
    Issue (Month): 1 (April)
    Pages: 71-108

    as in new window
    Handle: RePEc:eee:jmvana:v:65:y:1998:i:1:p:71-108

    Contact details of provider:
    Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information:
    Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=622892&ref=622892_01_ooc_1&version=01

    Related research

    Keywords: heteroscadicity; weighted linear regression;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Amemiya, Takeshi, 1983. "Non-linear regression models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 6, pages 333-389 Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:65:y:1998:i:1:p:71-108. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.