Robust principal component analysis
Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure of principal component analysis (PCA) which works well with respect to grossly corrupted observati
Two-step M-estimator
Two-step M-estimators deals with M-estimation problems that require preliminary estimation to obtain the parameter of interest. Two-step M-estimation is different from usual M-estimation problem becau
Bagplot
A bagplot, or starburst plot, is a method in robust statistics for visualizing two- or three-dimensional statistical data, analogous to the one-dimensional box plot. Introduced in 1999 by Rousseuw et
Interquartile mean
The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in spo
Simplicial depth
In robust statistics and computational geometry, simplicial depth is a measure of central tendency determined by the simplices that contain a given point. For the Euclidean plane, it counts the number
CDF-based nonparametric confidence interval
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculat
Least absolute deviations
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical opti
Winsorized mean
A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after win
Median absolute deviation
In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated b
Outlier
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter
Trimmed estimator
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust s
Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be th
Influential observation
In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regre
Nonparametric statistics
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparame
L-estimator
In statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as i
Least trimmed squares
Least trimmed squares (LTS), or least trimmed sum of squares, is a robust statistical method that fits a function to a set of data whilst not being unduly affected by the presence of outliers. It is o
Weighted median
In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust
Winsorizing
Winsorizing or winsorization is the transformation of statistics by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers. It is named after the engineer-t
Truncated mean
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability dist
Convex layers
In computational geometry, the convex layers of a set of points in the Euclidean plane are a sequence of nested convex polygons having the points as their vertices. The outermost one is the convex hul
Robust measures of scale
In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the inte
Robust Bayesian analysis
In statistics, robust Bayesian analysis, also called Bayesian sensitivity analysis, is a type of sensitivity analysis applied to the outcome from Bayesian inference or Bayesian optimal decisions.
Robust statistics
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have
Trimean
In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: This is equi
M-estimator
In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special c
Hodges–Lehmann estimator
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter. For populations that are symmetric about one median, such as the (Gaussian) no
Dixon's Q test
In statistics, Dixon's Q test, or simply the Q test, is used for identification and rejection of outliers. This assumes normal distribution and per Robert Dean and Wilfrid Dixon, and others, this test
Redescending M-estimator
In statistics, redescending M-estimators are Ψ-type M-estimators which have ψ functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ψ functions can be c
Medcouple
In statistics, the medcouple is a robust statistic that measures the skewness of a univariate distribution. It is defined as a scaled median difference of the left and right half of a distribution. It
Info-gap decision theory
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a g
Random sample consensus
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers, when outliers are to be accorded no influence
Huber loss
In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used.