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Example: M-Estimators for Robust Linear Modeling

M-Estimators for Robust Linear Modeling

In [1]:
%matplotlib inline

from __future__ import print_function
from statsmodels.compat import lmap
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

import statsmodels.api as sm
  • An M-estimator minimizes the function
$$Q(e_i, \rho) = \sum_i~\rho \left (\frac{e_i}{s}\right )$$

where $\rho$ is a symmetric function of the residuals

  • The effect of $\rho$ is to reduce the influence of outliers
  • $s$ is an estimate of scale.
  • The robust estimates $\hat{\beta}$ are computed by the iteratively re-weighted least squares algorithm
  • We have several choices available for the weighting functions to be used
In [2]: