## Quick Reference

*M*-estimates are measures of location that are not as sensitive as the mean to outlier values. With observations *x*_{1}, *x*_{2},…, *x** _{n}*, the sample mean can be characterized as the value of

*θ*that minimizes , where g(

*u*)=

*u*

^{2}. The sample median can be characterized in a similar way, though now g(

*u*)=|

*u*|.

*M*-estimates can be characterized in this same way, but the functional forms for g are chosen to be less sensitive to outlier values. One frequently used alternative as a measure of location is the Huber function: where *k* is a tuning constant (often set equal to twice the median absolute deviation).

A second alternative is the biweight function: where *k* is again a tuning constant and is here often set equal to seven times the median absolute deviation. See also *L*-estimate.

**From:**
M-estimate
in
A Dictionary of Statistics »

*Subjects:*
Probability and Statistics.

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