Robust Linear Models

Robust linear models with support for the M-estimators listed under Norms.

See Module Reference for commands and arguments.

Examples

# Load modules and data
In [1]: import statsmodels.api as sm

ImportErrorTraceback (most recent call last)
<ipython-input-1-6030a6549dc0> in <module>()
----> 1 import statsmodels.api as sm

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/api.py in <module>()
      5 from . import regression
      6 from .regression.linear_model import OLS, GLS, WLS, GLSAR
----> 7 from .regression.recursive_ls import RecursiveLS
      8 from .regression.quantile_regression import QuantReg
      9 from .regression.mixed_linear_model import MixedLM

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/regression/recursive_ls.py in <module>()
     14 from statsmodels.regression.linear_model import OLS
     15 from statsmodels.tools.data import _is_using_pandas
---> 16 from statsmodels.tsa.statespace.mlemodel import (
     17     MLEModel, MLEResults, MLEResultsWrapper)
     18 from statsmodels.tools.tools import Bunch

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/tsa/statespace/mlemodel.py in <module>()
     12 from scipy.stats import norm
     13 
---> 14 from .kalman_smoother import KalmanSmoother, SmootherResults
     15 from .kalman_filter import (KalmanFilter, FilterResults, INVERT_UNIVARIATE,
     16                             SOLVE_LU)

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/tsa/statespace/kalman_smoother.py in <module>()
     12 import numpy as np
     13 
---> 14 from statsmodels.tsa.statespace.representation import OptionWrapper
     15 from statsmodels.tsa.statespace.kalman_filter import (KalmanFilter,
     16                                                       FilterResults)

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/tsa/statespace/representation.py in <module>()
      8 
      9 import numpy as np
---> 10 from .tools import (
     11     find_best_blas_type, prefix_dtype_map, prefix_statespace_map,
     12     validate_matrix_shape, validate_vector_shape

/builddir/build/BUILD/statsmodels-0.8.0/statsmodels/tsa/statespace/tools.py in <module>()
     10 from scipy.linalg import solve_sylvester
     11 from statsmodels.tools.data import _is_using_pandas
---> 12 from . import _statespace
     13 
     14 has_find_best_blas_type = True

ImportError: cannot import name _statespace

In [2]: data = sm.datasets.stackloss.load()

NameErrorTraceback (most recent call last)
<ipython-input-2-ce15c2d6cff3> in <module>()
----> 1 data = sm.datasets.stackloss.load()

NameError: name 'sm' is not defined

In [3]: data.exog = sm.add_constant(data.exog)

NameErrorTraceback (most recent call last)
<ipython-input-3-528ff98c77bc> in <module>()
----> 1 data.exog = sm.add_constant(data.exog)

NameError: name 'sm' is not defined

# Fit model and print summary
In [4]: rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())

NameErrorTraceback (most recent call last)
<ipython-input-4-9a0676ae2e1a> in <module>()
----> 1 rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())

NameError: name 'sm' is not defined

In [5]: rlm_results = rlm_model.fit()

NameErrorTraceback (most recent call last)
<ipython-input-5-faa1c6d417e5> in <module>()
----> 1 rlm_results = rlm_model.fit()

NameError: name 'rlm_model' is not defined

In [6]: print(rlm_results.params)

NameErrorTraceback (most recent call last)
<ipython-input-6-e6f861521b3a> in <module>()
----> 1 print(rlm_results.params)

NameError: name 'rlm_results' is not defined

Detailed examples can be found here:

Technical Documentation

References

  • PJ Huber. ‘Robust Statistics’ John Wiley and Sons, Inc., New York. 1981.
  • PJ Huber. 1973, ‘The 1972 Wald Memorial Lectures: Robust Regression: Asymptotics, Conjectures, and Monte Carlo.’ The Annals of Statistics, 1.5, 799-821.
  • R Venables, B Ripley. ‘Modern Applied Statistics in S’ Springer, New York,

Module Reference

Model Classes

RLM(endog, exog[, M, missing]) Robust Linear Models

Model Results

RLMResults(model, params, ...) Class to contain RLM results

Norms

AndrewWave([a]) Andrew’s wave for M estimation.
Hampel([a, b, c]) Hampel function for M-estimation.
HuberT([t]) Huber’s T for M estimation.
LeastSquares Least squares rho for M-estimation and its derived functions.
RamsayE([a]) Ramsay’s Ea for M estimation.
RobustNorm The parent class for the norms used for robust regression.
TrimmedMean([c]) Trimmed mean function for M-estimation.
TukeyBiweight([c]) Tukey’s biweight function for M-estimation.
estimate_location(a, scale[, norm, axis, ...]) M-estimator of location using self.norm and a current estimator of scale.

Scale

Huber([c, tol, maxiter, norm]) Huber’s proposal 2 for estimating location and scale jointly.
HuberScale([d, tol, maxiter]) Huber’s scaling for fitting robust linear models.
mad(a[, c, axis, center]) The Median Absolute Deviation along given axis of an array
hubers_scale Huber’s scaling for fitting robust linear models.
stand_mad(a[, c, axis])