Nonparametric Statistics with Applications to Science and Engineering with R, 2nd Edition

13Curve Fitting Techniques

“Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose.”

J.B.S. Haldane (Haldane's Law)

In this chapter, we will learn about a general class of nonparametric regression techniques that fit a response curve to input predictors without making strong assumptions about error distributions. The estimators, called smoothing functions, actually can be smooth or bumpy as the user sees fit. The final regression function can be made to bring out from the data what is deemed to be important to the analyst. Plots of a smooth estimator will give the user a good sense of the overall trend between the input and the response . However, interesting nuances of the data might be lost to the eye. Such details will be more apparent with less smoothing, but a potentially noisy and jagged curve plotted made to catch such details might hide the overall trend of the data. Because no linear form is assumed in the model, this nonparametric regression approach is also an important component of nonlinear regression, which can also be parametric.

Let be a set of independent pairs of observations from the bivariate random ...