Comparison of nonlinear curves and surfaces

Area of Science:

• Statistics
• Nonparametric Regression Analysis
• Computational Statistics

Background:

• Nonlinear curve and surface estimation is a key area in semiparametric and nonparametric regression.
• Comparison of nonlinear functions remains less explored, with existing methods having limitations.
• Lack of readily available computational tools hinders nonlinear function comparisons.

Purpose of the Study:

• To propose novel statistical testing procedures for comparing nonlinear curves and surfaces.
• To develop user-friendly computational tools for implementing these new tests.
• To address the limitations of existing comparative procedures in nonlinear regression.

Main Methods:

• Development of two modified testing procedures for nonlinear function comparisons.
• Implementation of these procedures in an R package with familiar syntax.
• Creation of an R Shiny application for interactive use by non-R users.

Main Results:

• The proposed tests demonstrate consistency against fixed alternative hypotheses.
• Performance of the new tests is evaluated against existing methods.
• The methods are illustrated with practical applications using real-world data.

Conclusions:

• The study provides enhanced statistical tools for nonlinear function comparison.
• The developed R package and Shiny application improve accessibility and usability.
• The new methods offer a consistent and practical approach to analyzing complex nonlinear data.