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.

中文翻译：

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非线性曲线和曲面的比较


非线性曲线和曲面的估计长期以来一直是半参数和非参数回归分析的焦点。研究较少的是非线性函数的比较。在低维情况下，推理通常涉及曲线和曲面的比较。现有的比较程序受到各种限制，并且很少有计算工具可供现成使用。为了解决这些限制，提出了两种用于非线性曲线和曲面比较的改进测试程序。所提出的计算工具在 R 包中实现，其语法类似于常用的模型拟合包。 R Shiny 应用程序为不使用 R 的分析师提供了一个交互式界面。新的测试与固定的替代假设是一致的。理论细节在附录中给出。所提出的测试的操作特性是根据现有方法进行评估的。通过实际数据示例说明了这些方法的应用。