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Robust Linear Models

Introduction

Robust linear models with support for the M-estimators listed under norms.

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,

Examples

import statsmodels.api as sm
data = sm.datasets.stackloss.load()
data.exog = sm.add_constant(data.exog)
rlm_model = sm.RLM(data.endog, data.exog, M=sm.robust.norms.HuberT())
rlm_results = rlm_model.fit()
print rlm_results.params

see also the examples and the tests folders

Module Reference

Model and Result Classes

RLM(endog, exog[, M]) Robust Linear Models
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]) 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]) The standardized Median Absolute Deviation along given axis of an array.

Technical Documentation