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| 中央絶対偏差 (MAD) 推定× | SnおよびQnロバストスケール推定量× | |
|---|---|---|
| 分野 | 統計学 | 統計学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1974 | 1993 |
| 提唱者≠ | Hampel (influence-curve treatment); classical robust statistics | Rousseeuw & Croux |
| 種類 | Robust scale estimator | Robust scale estimator |
| 原典≠ | Hampel, F. R. (1974). The Influence Curve and Its Role in Robust Estimation. Journal of the American Statistical Association, 69(346), 383-393. DOI ↗ | Rousseeuw, P. J., & Croux, C. (1993). Alternatives to the Median Absolute Deviation. Journal of the American Statistical Association, 88(424), 1273-1283. DOI ↗ |
| 別名≠ | median absolute deviation, MAD scale estimator, robust scale estimation, Medyan Mutlak Sapma (MAD) Tahmini | Sn estimator, Qn estimator, Rousseeuw-Croux scale estimators, robust scale estimation |
| 関連 | 5 | 5 |
| 概要≠ | Median Absolute Deviation estimation is a robust measure of statistical dispersion that replaces the standard deviation when outliers are present. Rooted in the influence-curve framework formalised by Hampel (1974), it summarises the spread of a continuous variable using medians instead of means, so a single extreme value cannot distort the result. | Sn and Qn are robust estimators of scale (spread) proposed by Rousseeuw and Croux (1993) as alternatives to the median absolute deviation (MAD). Both attain a 50% breakdown point while delivering higher statistical efficiency than MAD, so they measure dispersion accurately even when the data contain outliers. |
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