# A different MSE criterion

I need to use the criterion

$$\text{MSE}=(\hat\beta-\beta)^T\,V\,(\hat\beta-\beta)$$

for a linear regression model to estimate the test MSE. Here $$\beta$$'s are the regression parameters and $$V$$ is the population covariance matrix. I have to split the data

• train (to estimate $$\beta$$'s)

• validation (to estimate hyperparameters) and

• test sets (to estimate Test MSE).

But the criterion given above does not include any term about the test set.

How could I use this criterion to estimate the test MSE?

• I know that definition of Test MSE. But I have to use the criterion in the question. There are some papers using this criterion and I have to do the same for a simulation study. – mert Oct 22 '18 at 8:29