Symmetric mean squared error
AmP estimation  


For each entry a Symmetric Mean Squared Error (SMSE) is computed to help judge the goodness of fit.
Definition
To compute the SMSE we start by computing the Symmetric Squared Error (SSE) for each data set. The SSE of a data set is computed in this way
where i refers to the data set and j to a given point in data set i. d_{ij} stands for the data, p_{ij} for the model prediction and w_{ij} for the associated weight coefficient. Finally, d_{i} and p_{i} in the denominator represent, respectively, the average of all data points (d_{ij}) and predictions (p_{ij}) in set i:
In the case the sum of the weights w_{i} is equal to zero we simply take the error to be zero. The implication is that this data set does not contribute to the SMSE.
SMSE is then the mean of all SSE_{i} with w_{i} greater than 0.
where n' is the number of data sets with w_{i} greater than 0.
The zerovariate case
In the case of a zerovariate data set the relative error simplifies to
and the connection with the formal definition of relative is more easily seen.