Browsing by Subject "Nonparametric and semiparametric regression"

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    Comparison of nonlinear curves and surfaces
    (Elsevier, 2020-10) Zhao, Shi; Bakoyannis, Giorgos; Lourens, Spencer; Tu, Wanzhu; Biostatistics, School of Public Health
    Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression analysis. What has been less studied is the comparison of nonlinear functions. In lower-dimensional situations, inference typically involves comparisons of curves and surfaces. The existing comparative procedures are subject to various limitations, and few computational tools have been made available for off-the-shelf use. To address these limitations, two modified testing procedures for nonlinear curve and surface comparisons are proposed. The proposed computational tools are implemented in an R package, with a syntax similar to that of the commonly used model fitting packages. An R Shiny application is provided with an interactive interface for analysts who do not use R. The new tests are consistent against fixed alternative hypotheses. Theoretical details are presented in an appendix. Operating characteristics of the proposed tests are assessed against the existing methods. Applications of the methods are illustrated through real data examples.
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    Statistical comparisons for nonlinear curves and surfaces
    (2018-05-31) Zhao, Shi; Tu, Wanzhu; Bakoyannis, Giorgos; Lourens, Spencer; Song, Yiqing
    Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression. The advances in related model fitting methodology have greatly enhanced the analyst’s modeling flexibility and have led to scientific discoveries that would be otherwise missed by the traditional linear model analysis. What has been less forthcoming are the testing methods concerning nonlinear functions, particularly for comparisons of curves and surfaces. Few of the existing methods are carefully disseminated, and most of these methods are subject to important limitations. In the implementation, few off-the-shelf computational tools have been developed with syntax similar to the commonly used model fitting packages, and thus are less accessible to practical data analysts. In this dissertation, I reviewed and tested the existing methods for nonlinear function comparison, examined their operational characteristics. Some theoretical justifications were provided for the new testing procedures. Real data exampleswere included illustrating the use of the newly developed software. A new R package and a more user-friendly interface were created for enhanced accessibility.