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, ...[, cov])

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
`MQuantileNorm`(q, base_norm)	M-quantiles objective function based on a base norm
`RamsayE`([a])	Ramsay's Ea for M estimation
`RobustNorm`()	The parent class for the norms used for robust regression
`StudentT`([c, df])	Robust norm based on t distribution
`TrimmedMean`([c])	Trimmed mean function for M-estimation
`TukeyBiweight`([c])	Tukey's biweight function for M-estimation
`TukeyQuartic`([c, k])	Variant of Tukey's biweight function with power 4 for M-estimation
`estimate_location`(a, scale[, norm, axis, ...])	Estimate a robust location parameter using an M-estimator.

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
`MScale`(chi_func, scale_bias)	M-scale estimation
`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
`scale_tau`(data[, cm, cs, weight_mean, ...])	Tau estimator of univariate scale
`scale_trimmed`(data, alpha[, center, axis, ...])	Scale estimate based on symmetrically trimmed sample

Deterministic-Start Robust Covariance Estimation#

Robust estimators of multivariate location and scatter, including the minimum covariance determinant (MCD) and S-estimators with deterministic (non-random) starting values.

`CovM`(data[, norm_mean, norm_scatter, ...])	M-estimator for multivariate Mean and Scatter
`CovDetMCD`(data)	Minimum covariance determinant estimator with deterministic starts
`CovDetS`(data[, norm, breakdown_point])	S-estimator for mean and covariance with deterministic starts
`CovDetMM`(data[, norm, breakdown_point, ...])	MM estimator using DetS as first stage estimator

Resistant (Deterministic-Start) Regression#

Regression M- and MM-estimators using S-estimator starting values computed deterministically, rather than through random resampling.

`RLMDetS`(endog, exog[, norm, ...])	S-estimator for linear model with deterministic starts.
`RLMDetSMM`(endog, exog[, norm, efficiency, ...])	MM-estimator with S-estimator starting values.