On a property of the expected value of a determinant
Suppose that the vectors x1, ..., xN in RP are i.i.d. with some underlying distribution [mu], and consider the matrix MN=(1/N)[summation operator]Ni=1xixTi. We show that, with constant C(N, p) = N!/(Np(N - p)!) not depending on [mu], the expected value of the determinant is of MN is proportional to the determinant of the expected value of MN. This implies, in particular, that in a linear regression problem with regressors independently generated with a measure [mu], the measure maximizing the expected value of the determinant of the information matrix is D-optimal, whatever the number of observations.
Year of publication: |
1998
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Authors: | Pronzato, L. |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 39.1998, 2, p. 161-165
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Publisher: |
Elsevier |
Keywords: | Expected value Determinant Optimal design D-optimality Linear regression |
Saved in:
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