Our program of research has contributed to the theory and applications of linear, nonlinear parametric, and nonparametric regression

As discussed in the context of conventional OLS regression modelling, regression analysis estimates the conditional expectation of a response given predictor variables. The conditional expectation is called the regression function and is the best predictor of the response based on the predictor variables because it minimizes the expected squared prediction error.

As Ruppert and Matteson (2015) state in their book Nonparametric Regression and Splines, there are three types of regression: linear, nonlinear parametric, and nonparametric.

• Linear regression assumes that the regression function is a linear function of the parameters and estimates the intercept and slopes (regression coefficients).
• Nonlinear parametric regression does not assume linearity but does assume that the regression function is of a known parametric form.
• For nonparametric regression the form of the regression function is also nonlinear but, unlike nonlinear parametric regression, not specified by a model but rather determined from the data. Nonparametric regression is used when we know, or suspect, that the regression function is curved, but we do not have a model for the curve.

Ruppert, D., Matteson, D.S. (2015). Nonparametric Regression and Splines. In: Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. Springer