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Extreme Value Theory
Branch of statistics studying the asymptotic behaviors of distribution extremes, enabling the modeling and prediction of rare events of large magnitude.
Robust Statistics
Set of statistical methods resistant to assumption violations and extreme values, providing reliable estimates even in the presence of contaminated data.
Winsorization
Statistical transformation technique replacing extreme values with specified quantiles, thus limiting the influence of outlier observations on the analysis.
Cook's Distance
Influence measure in regression identifying observations with a disproportionate impact on the estimated model parameters, combining leverage and residuals.
Leverage Points
Observations with extreme predictor values that can exert excessive influence on regression coefficients, even if they follow the expected model.
Breakdown Point
Minimum proportion of contamination that a statistical estimator can tolerate before producing arbitrarily incorrect results, measuring the robustness of a method.
DBSCAN Clustering
Density-based clustering algorithm capable of automatically identifying clusters of arbitrary shapes and noise points as extreme values.
Grubbs' Test
Parametric statistical test for detecting a single outlier in normally distributed data, based on standardized standard deviations.
Extreme Percentile Method
Approach identifying extreme values based on the upper or lower percentiles of the distribution, commonly using the extreme 1% or 5% as threshold.
Median Absolute Deviation
Robust measure of dispersion calculated from median absolute deviations, resistant to extreme values and alternative to standard deviation.
Influential Observations
Data points whose presence or absence significantly alters the results of a statistical analysis, detected by measures such as Cook's distance.
Tukey's Fences
Method for detecting extreme values using boundaries based on the interquartile range, typically 1.5*IQR for moderate values and 3*IQR for extremes.
Chauvenet's Criterion
Classical statistical test identifying outliers based on the probability of occurrence of an observation in an assumed normal distribution.