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Condition numbers and D-efficiency

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  • Jensen, D. R.

Abstract

Suppose that experimental designs have comparable A-efficiencies for estimation, the choice among designs then depending on their comparative D-efficiencies. Using the theory of majorization, it is shown that designs having greater D-efficiencies are more ill-conditioned, using condition numbers based on the unitarily invariant matrix norms. Implications are drawn regarding ridge regression, Mauchly (1940) sphericity criterion, and the structure of joint confidence regions for principal functions of the parameters. A case study treats alternative designs for estimating parameters of a second-order response model.

Suggested Citation

  • Jensen, D. R., 2004. "Condition numbers and D-efficiency," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 267-274, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:267-274
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