# Mean signed difference

34,202pages on
this wiki

### Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

In statistics, the mean signed difference (MSD), also known as mean signed error (MSE), is a sample statistic that summarises how well an estimator $\hat{\theta}$ matches the quantity $\theta$ that it is supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error.

## DefinitionEdit

The mean signed difference is derived from a set of n pairs, $( \hat{\theta}_i,\theta_i)$, where $\hat{\theta}_i$ is an estimate of the parameter $\theta$ in a case where it is known that $\theta=\theta_i$. In many applications, all the quantities $\theta_i$ will share a common value. When applied to forecasting in a time series analysis context, a forecasting procedure might be evaluated using the mean signed difference, with $\hat{\theta}_i$ being the predicted value of a series at a given lead time and $\theta_i$ being the value of the series eventually observed for that time-point. The mean signed difference is defined to be

$\operatorname{MSD}(\hat{\theta}) = \sum^{n}_{i=1} \frac{\hat{\theta_{i}} - \theta_{i}}{n} .$