# What is a loss function in decision theory?

My notes define a loss function as the 'cost' incurred when the true value of $\theta$ is estimated by $\hat\theta$. What kind of cost is it talking about? monetary cost? or is it something related to errors?

• Loss could be monetary, but is far more general. You could think of it as something akin to utility, but it doesn't have to be actual utility, or even very much like it. It's just some specifies measure of the 'badness' of the outcome in some sense. – Glen_b -Reinstate Monica Oct 19 '13 at 14:03

Simple examples of a loss function arise when we consider the difference between some true or correct value $\theta$ and an estimate $\hat\theta$, which you would like to be as small as possible. Possible ways of taking that further are to work with $(\theta - \hat\theta)^2$ or $|\theta - \hat\theta|$, which are both loss functions. In either case there is a minimum loss of 0 when $\hat\theta = \theta$.