A stand-alone Theil-Sen estimator for robust simple regression in Matlab.
(Stand-alone: No toolbox required.)
("Stand-alone" means that no toolbox is required.)
### Theil-Sen estimator
A [Theil-Sen estimator](https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator) provides robust, simple linear regression in the 2D plane:
A [Theil-Sen estimator](https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator) provides robust linear regression for one predictor:
The resulting estimates of slope and intercept are relatively insensitive to outliers.
The implementation of[TheilSen.m](TheilSen.m) is exact but naïve:
The implementation in[TheilSen.m](TheilSen.m) is exact but naïve:
It generates the set of all pairs of the _n_ input samples, resulting in an overall complexity of _O(n²)_ in speed and space.
The resulting slope and offset are the median slope and offset of the lines defined by all data point pairs.
(Note that alternative implementations of the algorithm have lower complexity, and thus much faster for large amounts of input samples.)
(Note that alternative implementations of the algorithm have lower complexity, and are thus much faster for large amounts of input samples.)
### No toolbox required
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@@ -23,8 +23,8 @@ This code is based on [Theil-Sen Robust Linear Regression](https://mathworks.com
A key modification is to use `median(X, 'omitnan')` instead of `nanmedian(X)` to avoid dependency on the (commercially licensed) [Statistics Toolbox](https://mathworks.com/products/statistics.html).
See the [changelog](#changelog) below for further modifications.
(Note that there are several other implementations of the Theil-Sen estimator on Mathworks's [File Exchange](https://mathworks.com/matlabcentral/fileexchange).
Unfortunately all were found to depend on the Statistics Toolbox, [except one](https://mathworks.com/matlabcentral/fileexchange/43135-regression-utilities), which was judged to be slower and less versatile.)
(Note that there are several other implementations on Mathworks's [File Exchange](https://mathworks.com/matlabcentral/fileexchange).
Unfortunately most were found to depend on the Statistics Toolbox, [except one](https://mathworks.com/matlabcentral/fileexchange/43135-regression-utilities), which was judged to be slower and less versatile.)
## Installation
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@@ -51,7 +51,9 @@ Note how a few "unlucky" outliers can bias the least squares estimate (LS), but
## Contributing and project status
This project is relatively unmaintained, and only shared as-is in the hope to be helpful.
This project is relatively unmaintained.
It is shared as-is in the hope to be helpful (see [license.txt](license.txt) for legal terms).
If you find a bug, feel free to let the author(s) know.
Feature requests should be directed to the original author (see below).
