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Median Absolute Deviation method
Robust statistic calculated as the median of absolute deviations from the median, used to measure dispersion while being resistant to extreme values.
M-estimator
Class of robust estimators obtained by minimizing a modified loss function that reduces the influence of outliers in parametric estimation.
Trimmed Mean
Mean calculated after removing a specified percentage of extreme values from both ends of the distribution, offering a robust measure of central tendency.
Robust quantile
Position measure calculated by linear interpolation or Harrell-Davis method, providing a stable estimation of quantiles even in the presence of data contamination.
Robust Mahalanobis distance
Multivariate distance measure using robust estimates of mean and covariance, enabling the detection of anomalies in high-dimensional spaces.
S-estimator
Robust scale estimator based on the median of absolute deviations weighted by a score function, offering an optimal compromise between efficiency and robustness.
Influence function
Mathematical tool measuring the impact of an infinitesimal contamination on an estimator, allowing quantification and comparison of the robustness of different statistical methods.
Redescending M-estimator
Variant of M-estimators whose weight function becomes zero beyond a certain threshold, completely eliminating the influence of extreme observations in the calculation.
MM-estimator
Robust estimator combining a high-breakdown M-estimator with a high-efficiency M-estimator, simultaneously optimizing robustness and statistical precision.
Tau-estimator
High-breakdown and high-efficiency scale estimator using a weighted combination of S and M estimators, particularly suited for skewed distributions.
R-estimator
Class of robust estimators based on the ranks of observations rather than their absolute values, offering invariance to monotonic transformations and natural resistance to outliers.
Weighted median absolute deviation
Variant of MAD incorporating weights based on the distance of observations to the center, improving anomaly detection in heterogeneous data.
Depth-based outlier detection
Robust approach identifying anomalies as points with the lowest statistical depth in the data cloud, measuring their relative central position.
Hampel identifier
Anomaly detection method based on median and MAD, classifying as outliers points that deviate by more than 3 median absolute deviations from the median.
Qn estimator
Robust scale estimator based on the median of pairwise absolute differences, offering 82% efficiency under normality and a 50% breakdown point.