kernreg 0.0.3

Tool for non-parametric curve fitting using local polynomials.

KernReg

KernReg provides a pure-Python routine for local polynomial kernel regression based on Wand & Jones (1995) and their accompanying R package KernSmooth. In addition, KernReg comes with an automatic bandwidth selection procedure that minimizes the residual squares criterion proposed by Fan & Gijbels (1996).

KernReg allows for the estimation of a regression function as well as their derivatives. The degree of the polynomial may be chosen ad libitum, but degree = derivative + 1 is commonly recommended and thus set by default.

Background

Local polynomial fitting provides a simple way of finding a functional relationship between two variables (where X typically denotes the predictor, and Y the response variable) without the imposition of a parametric model. It is a natural extension of local mean smoothing, as described by Nadaraya (1964) and Watson (1964). Instead of fitting a local mean, local polynomial smooting involves fitting a local pth-order polynomial via locally weighted least-squares. The Nadaraya–Watson estimator is thus equivalent to fitting a local polynomial of degree zero. Local polynomials of higher order have better bias properties and, in general, do not require bias adjustment at the boundaries of the regression space.

References

Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. Monographs on Statistics and Applied Probability, 66. Chapman & Hall.

Wand, M.P. & Jones, M.C. (1995). Kernel Smoothing. Monographs on Statistics and Applied Probability, 60. Chapman & Hall.

Wand, M.P. and Ripley, B. D. (2015). KernSmooth: Functions for Kernel Smoothing for Wand and Jones (1995). R package version 2.23-18.

---

* The image is taken from futurist illustrator Arthur Radebaugh's (1906–1974) Sunday comic strip Closer Than We Think!, which was published by the Chicago Tribune - New York News Syndicate from 1958 to 1963.