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
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:

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
`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])