Indiana University-Purdue University Indianapolis (IUPUI) / 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. / 2020-08-22