Relationship between D- and A- optimal design
$begingroup$
The "General Equivalence Theorem" states that a D-optimal design and G-optimal design are equivalent.
Is there any relationship (possibly under some non-trivial conditions) between a D-optimal design and an A-optimal design?
A D-optimal design has the smallest determinant of $(X^T X)^{-1}$ ... an A optimal design has the smallest trace of $(X^T X)^{-1}$.
The purpose of my question is: For a certain model I proofed that it is always D-optimal (as well as T optimal). However, I would be interested in the MSE of the coefficients (which is proportional to $operatorname{Tr} (X^T X)^{-1}$.
statistics
asked Jan 8 at 9:20
divBdivB
228111
$endgroup$
add a comment |
$begingroup$
The "General Equivalence Theorem" states that a D-optimal design and G-optimal design are equivalent.
Is there any relationship (possibly under some non-trivial conditions) between a D-optimal design and an A-optimal design?
A D-optimal design has the smallest determinant of $(X^T X)^{-1}$ ... an A optimal design has the smallest trace of $(X^T X)^{-1}$.
The purpose of my question is: For a certain model I proofed that it is always D-optimal (as well as T optimal). However, I would be interested in the MSE of the coefficients (which is proportional to $operatorname{Tr} (X^T X)^{-1}$.
statistics
asked Jan 8 at 9:20
divBdivB
228111
$endgroup$
add a comment |
$begingroup$
The "General Equivalence Theorem" states that a D-optimal design and G-optimal design are equivalent.
Is there any relationship (possibly under some non-trivial conditions) between a D-optimal design and an A-optimal design?
A D-optimal design has the smallest determinant of $(X^T X)^{-1}$ ... an A optimal design has the smallest trace of $(X^T X)^{-1}$.
The purpose of my question is: For a certain model I proofed that it is always D-optimal (as well as T optimal). However, I would be interested in the MSE of the coefficients (which is proportional to $operatorname{Tr} (X^T X)^{-1}$.
statistics
asked Jan 8 at 9:20
divBdivB
228111
$endgroup$
The "General Equivalence Theorem" states that a D-optimal design and G-optimal design are equivalent.
Is there any relationship (possibly under some non-trivial conditions) between a D-optimal design and an A-optimal design?
A D-optimal design has the smallest determinant of $(X^T X)^{-1}$ ... an A optimal design has the smallest trace of $(X^T X)^{-1}$.
The purpose of my question is: For a certain model I proofed that it is always D-optimal (as well as T optimal). However, I would be interested in the MSE of the coefficients (which is proportional to $operatorname{Tr} (X^T X)^{-1}$.
statistics
statistics
asked Jan 8 at 9:20
divBdivB
228111
asked Jan 8 at 9:20
divBdivB
228111
edited Jan 8 at 9:36
divB
asked Jan 8 at 9:20
divBdivB
228111
asked Jan 8 at 9:20
divBdivB
228111
asked Jan 8 at 9:20
divBdivB
228111
228111
add a comment |
add a comment |
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