Editing Loss function (section)

====Examples in statistics====
* For a scalar parameter ''θ'', a decision function whose output <math>\hat\theta</math> is an estimate of&nbsp;''θ'', and a quadratic loss function ([[squared error loss]]) <math display="block"> L(\theta,\hat\theta)=(\theta-\hat\theta)^2,</math> the risk function becomes the [[mean squared error]] of the estimate, <math display="block">R(\theta,\hat\theta)= \operatorname{E}_\theta \left [ (\theta-\hat\theta)^2 \right ].</math>An [[Estimator]] found by minimizing the [[Mean squared error]] estimates the [[Posterior distribution]]'s mean.
* In [[density estimation]], the unknown parameter is [[probability density function|probability density]] itself. The loss function is typically chosen to be a [[Norm (mathematics)|norm]] in an appropriate [[function space]]. For example, for [[L2 norm|''L''<sup>2</sup> norm]], <math display="block">L(f,\hat f) = \|f-\hat f\|_2^2\,,</math> the risk function becomes the [[mean integrated squared error]] <math display="block">R(f,\hat f)=\operatorname{E} \left ( \|f-\hat f\|^2 \right ).\,</math>