• Login
    View Item 
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    •   Home
    • Graduate Theses, Dissertations and Projects
    • Queen's Graduate Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Optimal design in regression and spline smoothing

    Thumbnail
    View/Open
    Cho_Jaerin_200707_PhD.pdf (662.0Kb)
    Date
    2007-07-19
    Author
    Cho, Jaerin
    Metadata
    Show full item record
    Abstract
    This thesis represents an attempt to generalize the classical Theory of Optimal Design to popular regression models, based on Rational and Spline approximations. The problem of finding optimal designs for such models can be reduced to solving certain minimax problems. Explicit solutions to such

    problems can be obtained only in a few selected models, such as polynomial regression.

    Even when an optimal design can be found, it has, from the point of view of modern nonparametric regression, certain drawbacks. For example, in the polynomial regression case, the optimal design crucially depends on the degree m of approximating polynomial.

    Hence, it can be used only when such degree is given/known in advance.

    We present a partial, but practical, solution to this problem. Namely, the so-called Super Chebyshev Design has been found, which does not depend on the degree m of the underlying

    polynomial regression in a large range of m, and at the same time is asymptotically more than 90% efficient. Similar results are obtained in the case of rational regression, even though the exact form of optimal design in this case remains unknown.

    Optimal Designs in the case of Spline Interpolation are also currently unknown. This problem, however, has a simple solution in the case of Cardinal Spline Interpolation. Until recently, this model has been practically unknown in modern nonparametric

    regression. We demonstrate the usefulness of Cardinal Kernel Spline Estimates in nonparametric regression, by proving their

    asymptotic optimality, in certain classes of smooth functions. In this way, we have found, for the first time, a theoretical justification of a well known empirical observation, by which cubic splines suffice, in most practical applications.
    URI for this record
    http://hdl.handle.net/1974/448
    Collections
    • Queen's Graduate Theses and Dissertations
    • Department of Mathematics and Statistics Graduate Theses
    Request an alternative format
    If you require this document in an alternate, accessible format, please contact the Queen's Adaptive Technology Centre

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV
     

     

    Browse

    All of QSpaceCommunities & CollectionsPublished DatesAuthorsTitlesSubjectsTypesThis CollectionPublished DatesAuthorsTitlesSubjectsTypes

    My Account

    LoginRegister

    Statistics

    View Usage StatisticsView Google Analytics Statistics

    DSpace software copyright © 2002-2015  DuraSpace
    Contact Us
    Theme by 
    Atmire NV