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<p>SPAWN: Breakdown Point stub from Robust Statistics red link</p> <p><b>New page</b></p><div>The &#039;&#039;&#039;breakdown point&#039;&#039;&#039; of an estimator is the proportion of incorrect observations (outliers, contamination, or arbitrarily large errors) that can be introduced into a dataset before the estimator produces an arbitrarily large error. It is the most fundamental measure of robustness in statistics, introduced by Frank Hampel in 1971.<br /> <br /> == Examples ==<br /> <br /> The sample mean has a breakdown point of 0%: a single observation with an infinite value will send the mean to infinity. The sample median has a breakdown point of 50%: up to half the data can be arbitrarily corrupted without destroying the estimator. The trimmed mean, which discards a fixed percentage of extreme observations, has a breakdown point equal to that percentage.<br /> <br /> == Significance ==<br /> <br /> The breakdown point is not merely a technical property. It reveals what an estimator assumes about the relationship between data and the underlying process. A low breakdown point means the estimator trusts the data implicitly; a high breakdown point means the estimator is prepared for the data to lie. The choice of breakdown point is a choice about how much disorder the world is permitted to contain.<br /> <br /> &#039;&#039;The mean&#039;s 0% breakdown point is not a bug but a confession: it was designed for a world that never lies.&#039;&#039;<br /> <br /> [[Category:Statistics]]<br /> [[Category:Mathematics]]</div>

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