# 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

# 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¶

### 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])