scipy.stats.

siegelslopes#

scipy.stats.siegelslopes(y, x=None, method='hierarchical', *, axis=None, nan_policy='propagate', keepdims=False)[source]#

Computes the Siegel estimator for a set of points (x, y).

siegelslopes implements a method for robust linear regression using repeated medians (see [1]) to fit a line to the points (x, y). The method is robust to outliers with an asymptotic breakdown point of 50%.

Parameters:

yarray_like

Dependent variable.

xarray_like or None, optional

Independent variable. If None, use arange(len(y)) instead.

method{‘hierarchical’, ‘separate’}

If ‘hierarchical’, estimate the intercept using the estimated slope slope (default option). If ‘separate’, estimate the intercept independent of the estimated slope. See Notes for details.

axisint or None, default: None

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy{‘propagate’, ‘omit’, ‘raise’}

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

keepdimsbool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

Returns:

resultSiegelslopesResult instance

The return value is an object with the following attributes:

slopefloat: Estimate of the slope of the regression line.
interceptfloat: Estimate of the intercept of the regression line.

See also

theilslopes: a similar technique without repeated medians

Notes

With n = len(y), compute m_j as the median of the slopes from the point (x[j], y[j]) to all other n-1 points. slope is then the median of all slopes m_j. Two ways are given to estimate the intercept in [1] which can be chosen via the parameter method. The hierarchical approach uses the estimated slope slope and computes intercept as the median of y - slope*x. The other approach estimates the intercept separately as follows: for each point (x[j], y[j]), compute the intercepts of all the n-1 lines through the remaining points and take the median i_j. intercept is the median of the i_j.

The implementation computes n times the median of a vector of size n which can be slow for large vectors. There are more efficient algorithms (see [2]) which are not implemented here.

For compatibility with older versions of SciPy, the return value acts like a namedtuple of length 2, with fields slope and intercept, so one can continue to write:

slope, intercept = siegelslopes(y, x)

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

References

[1] (1,2)

A. Siegel, “Robust Regression Using Repeated Medians”, Biometrika, Vol. 69, pp. 242-244, 1982.

[2]

A. Stein and M. Werman, “Finding the repeated median regression line”, Proceedings of the Third Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 409-413, 1992.

Examples

>>> import numpy as np
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

>>> x = np.linspace(-5, 5, num=150)
>>> y = x + np.random.normal(size=x.size)
>>> y[11:15] += 10  # add outliers
>>> y[-5:] -= 7

Compute the slope and intercept. For comparison, also compute the least-squares fit with linregress:

>>> res = stats.siegelslopes(y, x)
>>> lsq_res = stats.linregress(x, y)

Plot the results. The Siegel regression line is shown in red. The green line shows the least-squares fit for comparison.

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(x, y, 'b.')
>>> ax.plot(x, res[1] + res[0] * x, 'r-')
>>> ax.plot(x, lsq_res[1] + lsq_res[0] * x, 'g-')
>>> plt.show()

../../_images/scipy-stats-siegelslopes-1.png