Abstract
As discussed in Chap. 9, 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 upon the predictor variables, because it minimizes the expected squared prediction error.
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, which was discussed in Sect. 11.2, does not assume linearity but does assume that the regression function is of a known parametric form, for example, the Nelson-Siegel model. In this chapter, we study nonparametric regression, where 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.
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Notes
- 1.
The risk-free rate is called the risk-free return in the Capm package.
- 2.
“dpill” means “direct plug-in, local linear.”
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Ruppert, D., Matteson, D.S. (2015). Nonparametric Regression and Splines. In: Statistics and Data Analysis for Financial Engineering. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2614-5_21
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