M-estimator

M-estimator

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. 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. In many applications, such M-estimators can be thought of as estimating characteristics of the population.