7.4. Robust Linear Models¶
Robust linear models with support for the M-estimators listed under Norms.
See Module Reference for commands and arguments.
7.4.1. Examples¶
# Load modules and data
import statsmodels.api as sm
data = sm.datasets.stackloss.load()
data.exog = sm.add_constant(data.exog)
# Fit model and print summary
rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())
rlm_results = rlm_model.fit()
print rlm_results.params
Detailed examples can be found here:
7.4.2. Technical Documentation¶
7.4.2.1. 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,
7.4.3. Module Reference¶
7.4.3.2. Model Results¶
RLMResults(model, params, ...) |
Class to contain RLM results |
7.4.3.3. 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. |
7.4.3.4. 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 |
huber |
Huber’s proposal 2 for estimating location and scale jointly. |
hubers_scale |
Huber’s scaling for fitting robust linear models. |
stand_mad(a[, c, axis]) |