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-1-085740203b77> in <module>()
----> 1 import statsmodels.api as sm
/builddir/build/BUILD/statsmodels-0.9.0/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-0.9.0/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-0.9.0/statsmodels/tsa/statespace/mlemodel.py in <module>()
16 from scipy.stats import norm
17
---> 18 from .simulation_smoother import SimulationSmoother
19 from .kalman_smoother import SmootherResults
20 from .kalman_filter import (INVERT_UNIVARIATE, SOLVE_LU)
/builddir/build/BUILD/statsmodels-0.9.0/statsmodels/tsa/statespace/simulation_smoother.py in <module>()
8
9 import numpy as np
---> 10 from .kalman_smoother import KalmanSmoother
11 from . import tools
12
/builddir/build/BUILD/statsmodels-0.9.0/statsmodels/tsa/statespace/kalman_smoother.py in <module>()
9 import numpy as np
10
---> 11 from statsmodels.tsa.statespace.representation import OptionWrapper
12 from statsmodels.tsa.statespace.kalman_filter import (KalmanFilter,
13 FilterResults)
/builddir/build/BUILD/statsmodels-0.9.0/statsmodels/tsa/statespace/representation.py in <module>()
8
9 import numpy as np
---> 10 from .tools import (
11 find_best_blas_type, validate_matrix_shape, validate_vector_shape
12 )
/builddir/build/BUILD/statsmodels-0.9.0/statsmodels/tsa/statespace/tools.py in <module>()
205 'z': _statespace.zcopy_index_vector
206 })
--> 207 set_mode(compatibility=None)
208
209
/builddir/build/BUILD/statsmodels-0.9.0/statsmodels/tsa/statespace/tools.py in set_mode(compatibility)
57 if not compatibility:
58 from scipy.linalg import cython_blas
---> 59 from . import (_representation, _kalman_filter, _kalman_smoother,
60 _simulation_smoother, _tools)
61 compatibility_mode = False
ImportError: cannot import name _representation
In [2]: data = sm.datasets.stackloss.load()
NameErrorTraceback (most recent call last)
<ipython-input-2-39937126b887> 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-d96db36c0463> 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-4-3b4361066865> 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-f70735a6f6a2> 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-6-0a3000b32e1f> 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 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. |