Robust Variance Estimators (MAD, IQR-based)

Overview

When data contains outliers, classical variance estimators can be severely affected. Robust alternatives include the MAD and IQR-based estimators.

Median Absolute Deviation (MAD)

\[ \text{MAD} = \text{Median}(|X_i - \text{Median}(X)|) \]

For Normal data, \(\sigma \approx 1.4826 \cdot \text{MAD}\).

IQR-based Estimator

\[ \hat{\sigma}_{IQR} = \frac{\text{IQR}}{1.349} \]

Comparison

Estimator	Breakdown Point	Efficiency (Normal)
Sample variance	0%	100%
MAD	50%	37%
IQR-based	25%	37%