# scipy.stats.siegelslopes

scipy.stats.siegelslopes(y, x=None, method='hierarchical')

  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
    y array_like

      Dependent variable.

    x array_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 `medslope` (default option). If ‘separate’, estimate the intercept independent of the estimated slope. See Notes for details.

  Returns
    medslope float

      Estimate of the slope of the regression line.

    medintercept float

      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. `medslope` 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 `medslope` and computes `medintercept` as the median of `y - medslope*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`. `medintercept` 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.

  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

      >>> 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()

scipy.stats.linregress scipy.stats.theilslopes