A-optimality ("average" or trace)

One criterion is A-optimality, which seeks to minimize the trace of the inverse of the information matrix. This criterion results in minimizing the average variance of the estimates of the regression coefficients.

C-optimality

This criterion minimizes the variance of a best linear unbiased estimator of a predetermined linear combination of model parameters.

D-optimality (determinant)

A popular criterion is D-optimality, which seeks to minimize |(X'X)−1|, or equivalently maximize the determinant of the information matrix X'X of the design. This criterion results in maximizing the differential Shannon information content of the parameter estimates.

E-optimality (eigenvalue)

Another design is E-optimality, which maximizes the minimum eigenvalue of the information matrix.

T-optimality

This criterion maximizes the trace of the information matrix.

Other optimality-criteria are concerned with the variance of predictions:

G-optimality

A popular criterion is G-optimality, which seeks to minimize the maximum entry in the diagonal of the hat matrix X(X'X)−1X'. This has the effect of minimizing the maximum variance of the predicted values.

I-optimality (integrated)

A second criterion on prediction variance is I-optimality, which seeks to minimize the average prediction variance over the design space.

V-optimality (variance)

A third criterion on prediction variance is V-optimality, which seeks to minimize the average prediction variance over a set of m specific points.[9]

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