William J. J. Rey

Type M estimators

The type M estimators, also called M estimators, are generalizations of the usual maximum likelihood estimates. ϑ is classically the parameter value maximizing the likelihood function, i. e. we have in obvious notation

Quantile estimators and confidence intervals

L = \Pi f({x_i}|\vartheta ) = \max {\rm{for }}\vartheta

Bootstrap methods, sampling distributions

or equivalently

Type L estimators

- \ln {\rm{ }}L{\rm{ = - }}\sum {\rm{ ln }}f {\rm{(}}{x_i}|\vartheta ) = {\rm{ min for }}\vartheta {\rm{.}}

Type R estimator

The estimators of type M are solutions of the more general structure