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

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

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

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

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

In [6]: print(rlm_results.params)
[-41.0265   0.8294   0.9261  -0.1278]

Detailed examples can be found here:

• Robust Models 1
• Robust Models 2

Technical Documentation

• Weight Functions

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.