Module « scipy.stats »

Fonction siegelslopes - module scipy.stats

Signature de la fonction siegelslopes

def siegelslopes(y, x=None, method='hierarchical') 

Description

siegelslopes.__doc__

    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] 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()