Robust statistics

thumb|Calculating the median in data sets of odd (above) and even (below) observations The median of a set of numbers 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 thought of as the “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extreme values, and therefore provides a better representation of the center. Median income, for example, may be a better way to descri

thumb|Figure 1. Box plot of data from the [[Michelson–Morley experiment displaying four outliers in the middle column, as well as one outlier in the first column.]]

branch of statistics that is not based solely on parametrized families of probability distributions

statistics with good performance for data drawn from a wide range of probability distributions

statistical measure of central tendency

statistical method

median of the absolute deviation from the median; a robust measure of the variability of a univariate sample of quantitative data

statistical measure of central tendency that takes the mean of a winsorized dataset

The -medoids method is a classical partitioning technique of clustering that splits a data set of objects into clusters, where the number of clusters is assumed to be known a priori (which implies that the programmer must specify k before the execution of a -medoids algorithm). The "goodness" of the given value of can be assessed with methods such as the silhouette method. The name of the clustering method was coined by Leonard Kaufman and Peter J. Rousseeuw with their PAM (Partitioning Around Medoids) algorithm.

loss function used in robust regression

criterion for identification and rejection of outliers

robust and nonparametric estimator of a population's location parameter

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-turned-biostatistician Charles P. Winsor (1895–1951). The effect is the same as clipping in signal processing.

statistical optimality criterion

In statistics the trimean (TM), or '''Tukey's trimean''', is a measure of a probability distribution's central tendency defined as a weighted average of the distribution's quartiles: