https://github.com/segsell/kernreg
Tool for non-parametric curve fitting using local polynomials.
https://github.com/segsell/kernreg
curve-fitting kernel-regression local-polynomial-regression non-parametric
Last synced: 4 months ago
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Tool for non-parametric curve fitting using local polynomials.
- Host: GitHub
- URL: https://github.com/segsell/kernreg
- Owner: segsell
- License: mit
- Created: 2021-01-11T17:10:43.000Z (over 5 years ago)
- Default Branch: main
- Last Pushed: 2025-08-11T20:50:46.000Z (9 months ago)
- Last Synced: 2025-10-29T10:13:35.620Z (6 months ago)
- Topics: curve-fitting, kernel-regression, local-polynomial-regression, non-parametric
- Language: Python
- Homepage:
- Size: 901 KB
- Stars: 5
- Watchers: 1
- Forks: 0
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# KernReg
[](https://pypi.org/project/kernreg/)
[](https://pypi.org/project/kernreg)
[](https://kernreg.readthedocs.io/)
[](https://github.com/segsell/kernreg/actions?query=workflow%3A%22Continuous+Integration%22)
[](https://codecov.io/gh/segsell/kernreg)
[](https://www.codacy.com/gh/segsell/kernreg/dashboard?utm_source=github.com&utm_medium=referral&utm_content=segsell/kernreg&utm_campaign=Badge_Grade)
[](https://github.com/psf/black)
## Introduction
**KernReg** provides a pure-Python routine for local polynomial kernel regression based on [Wand & Jones (1995)](http://matt-wand.utsacademics.info/webWJbook/) and their accompanying *R* package [KernSmooth](https://www.rdocumentation.org/packages/KernSmooth/versions/2.23-18). In addition, **KernReg** comes with an automatic bandwidth selection procedure that minimizes the residual squares criterion proposed by [Fan & Gijbels (1996)](https://www.taylorfrancis.com/books/local-polynomial-modelling-applications-fan-gijbels/10.1201/9780203748725).
**KernReg** allows for the estimation of a regression function as well as their *v*th derivatives using the Gaussian density function as kernel weights. The degree of the polynomial *p* must be equal to ```v + 1```,
```v + 3```, ```v + 5```, or ```v + 7```.
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)](https://www.semanticscholar.org/paper/On-Estimating-Regression-Nadaraya/05175204318c3c01e3301fd864553071039605d2#paper-header) and [Watson (1964)](http://www.jstor.org/stable/25049340). Instead of fitting a local mean, local polynomial smooting involves fitting a local *p*th-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.
## Installation
Install **KernReg** via PyPI.
```console
$ pip install kernreg
```
## Quick-Start
```python
import kernreg as kr
motorcycle = kr.get_example_data()
x, y = motorcycle["time"], motorcycle["accel"]
# By default, only x and y need to be provided.
# Derivative = 0 is chosen by default
# and hence the polynomial degree = 0 + 1.
rslt_default = kr.locpoly(x, y)
kr.plot(x, y, rslt_default, "motorcycle_default_fit.png")
```
```python
# We can improve on the default specification by
# choosing a higher order polynomial
rslt_user = kr.locpoly(x, y, degree=3)
kr.plot(x, y, rslt_user, "motorcycle_user_fit.png")
```
## References
Fan, J. and Gijbels, I. (1996). [Local Polynomial Modelling and Its Applications](https://www.taylorfrancis.com/books/local-polynomial-modelling-applications-fan-gijbels/10.1201/9780203748725). *Monographs on Statistics and Applied Probability, 66*. Chapman & Hall.
Wand, M.P. & Jones, M.C. (1995). [Kernel Smoothing](http://matt-wand.utsacademics.info/webWJbook/). *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)](http://CRAN.R-project.org/package=KernSmooth). *R* package version 2.23-18.
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`*` The image is taken from futurist illustrator [Arthur Radebaugh's (1906–1974)](http://www.gavinrothery.com/my-blog/2012/7/15/arthur-radebaugh.html)
Sunday comic strip *Closer Than We Think!*, which was published by the Chicago Tribune - New York News Syndicate from 1958 to 1963.