Loosely, estimating a quantity by choosing it to be the extremum of a function, or, if it’s well-behaved enough, a zero of its derivative.

Popular with machine learning, where loss-function based methods are ubiquitous. In statistics we see this famously in maximum likelihood estimation and robust estimation, and least squares loss, for which M-estimation provides a unifying formalism with a convenient large sample asymptotic theory.

🏗 Discuss influence function motivation.

Implied density functions

Common loss function imply a density considered as a maximum_likelihood estimation problem.

Robust Loss functions


Huber loss

Hampel loss


Discuss representation (and implementation) in terms of weight functions for least-squares loss.


Mallows, Schweppe etc.



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