- published: 05 Mar 2015
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Robust statistics provides an alternative approach to standard statistical methods, such as those for estimating location, scale and regression parameters. The motivation is to produce estimators that are not unduly affected by small departures from the model assumptions under which these standard methods are usually derived: the standard methods are comparatively badly affected.
Robust statistics seeks to provide methods that emulate popular statistical methods, but which are not unduly affected by outliers or other small departures from model assumptions. In statistics, classical estimation methods rely heavily on assumptions which are often not met in practice. In particular, it is often assumed that the data errors are normally distributed, at least approximately, or that the central limit theorem can be relied on to produce normally distributed estimates. Unfortunately, when there are outliers in the data, classical estimators often have very poor performance, when judged using the breakdown point and the influence function, described below.
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