Comparison of nonlinear curves and surfaces

Shi Zhao, Giorgos Bakoyannis, Spencer Lourens, Wanzhu Tu

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number106987
JournalComputational Statistics and Data Analysis
Volume150
DOIs
StatePublished - Oct 2020

Keywords

  • Comparison of nonlinear functions
  • Nonparametric and semiparametric regression
  • Resampling methods

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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