# M-estimator Algorithm

An M-estimator Algorithm is a point estimation algorithm that searches for a minima of sums of functions of the data.

**See:**Least-Squares Estimator, Maximum Likelihood Estimation Algorithm, Continuous Optimization Algorithm.

## References

### 2012

- http://en.wikipedia.org/wiki/M-estimation
- In statistics,
**M-estimators**are a broad class of estimators, which are obtained as the minima of sums of functions of the data. Least-squares estimators and many maximum-likelihood estimators are M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. The statistical procedure of evaluating an M-estimator on a data set is called M-estimation.More generally, an M-estimator may be defined to be a zero of an estimating function.

^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}This estimating function is often the derivative of another statistical function: For example, a maximum-likelihood estimate is often defined to be a zero of the derivative of the likelihood function with respect to the parameter: thus, a maximum-likelihood estimator is often a critical point of the score function.^{[7]}In many applications, such M-estimators can be thought of as estimating characteristics of the population.

- In statistics,

- ↑ V. P. Godambe, editor.
*Estimating functions*, volume 7 of Oxford Statistical Science Series. The Clarendon Press Oxford University Press, New York, 1991. - ↑ Christopher C. Heyde.
*Quasi-likelihood and its application: A general approach to optimal parameter estimation*. Springer Series in Statistics. Springer-Verlag, New York, 1997. - ↑ D. L. McLeish and Christopher G. Small.
*The theory and applications of statistical inference functions*, volume 44 of Lecture Notes in Statistics. Springer-Verlag, New York, 1988. - ↑ Parimal Mukhopadhyay.
*An Introduction to Estimating Functions*. Alpha Science International, Ltd, 2004. - ↑ Christopher G. Small and Jinfang Wang.
*Numerical methods for nonlinear estimating equations*, volume 29 of Oxford Statistical Science Series. The Clarendon Press Oxford University Press, New York, 2003. - ↑ Sara A. van de Geer.
*Empirical Processes in M-estimation: Applications of empirical process theory,*volume 6 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2000. - ↑ Ferguson, Thomas S. (1982). "An inconsistent maximum likelihood estimate".
*Journal of the American Statistical Association***77**(380): 831–834. JSTOR 2287314.