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)
const       -41.026498
AIRFLOW       0.829384
WATERTEMP     0.926066
ACIDCONC     -0.127847
dtype: float64

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,
C Croux, PJ Rousseeuw, ‘Time-efficient algorithms for two highly robust estimators of scale’ Computational statistics. Physica, Heidelberg, 1992.

Module Reference¶

Model Classes¶

RLM(endog, exog[, M, missing])

Robust Linear Model

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.
`iqr`(a[, c, axis])	The normalized interquartile range along given axis of an array
`qn_scale`(a[, c, axis])	Computes the Qn robust estimator of scale