Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly.[1][2]
^Sarkar, Palash (2014-05-01). "On some connections between statistics and cryptology". Journal of Statistical Planning and Inference. 148: 20–37. doi:10.1016/j.jspi.2013.05.008. ISSN 0378-3758.
^Huber, Peter J.; Ronchetti, Elvezio M. (2009-01-29). Robust Statistics. Wiley Series in Probability and Statistics (1 ed.). Wiley. doi:10.1002/9780470434697. ISBN 978-0-470-12990-6.
Robuststatistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust statistical methods...
Hettmansperger, T. P.; McKean, J. W. (1998). Robust Nonparametric Statistical Methods. Kendall's Library of Statistics. Vol. 5. London: Edward Arnold. ISBN 0-340-54937-8...
the median. For this reason, the median is of central importance in robuststatistics. The median of a finite list of numbers is the "middle" number, when...
In robuststatistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship...
related to two other developments in statistical theory: robuststatistics and nonparametric statistics, both of which tried to reduce the sensitivity of statistical...
case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions,...
In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The...
mean may not coincide with one's notion of "middle". In that case, robuststatistics, such as the median, may provide a better description of central tendency...
probability and statisticsStatistics education World Statistics Day Robuststatistics Foundations and major areas of statistics Philosophy of statistics Probability...
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...
determine the best rules to use under given circumstances. However, in robuststatistics, statistical theory goes on to consider the balance between having...
Specifically, the PMCC is neither distributionally robust, nor outlier resistant (see Robuststatistics § Definition). Inspection of the scatterplot between...
Robust Principal Component Analysis (RPCA) is a modification of the widely used statistical procedure of principal component analysis (PCA) which works...
1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related...
deviation Ordinary least squares Robust regression "Least Absolute Deviation Regression". The Concise Encyclopedia of Statistics. Springer. 2008. pp. 299–302...
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...
(which are defined below). Elliptical distributions are also used in robuststatistics to evaluate proposed multivariate-statistical procedures. Elliptical...
values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators...
Trimmed estimator Huber loss Robust regression Andri Signorell et al. (2021). DescTools: Tools for descriptive statistics. R package version 0.99.41. Lee...
(but useless) comments I hear is that some solutions can come from 'robuststatistics.' I wonder how using these techniques can create information where...
Robust Regression and Outlier Detection is a book on robuststatistics, particularly focusing on the breakdown point of methods for robust regression....
robust critique of non-robuststatistics, often derived from pivotal quantities: such statistics may be robust within the family, but are not robust outside...
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