/Statsmodels

# 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 : import statsmodels.api as sm

In : data = sm.datasets.stackloss.load()

In : data.exog = sm.add_constant(data.exog)

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

In : rlm_results = rlm_model.fit()

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

Detailed examples can be found here:

## Technical Documentation

• 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.

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor