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A minimax equivalence theorem for optimum bounded design measures

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  • Pronzato, Luc

Abstract

For [mu] a given measure and [phi](·) a regular optimality criterion, function of the information matrix, we consider [phi]-optimum design measures [xi][alpha]* that maximise [phi] under the constraint [xi][alpha]*[less-than-or-equals, slant][mu]/[alpha], [alpha] given in (0,1). We derive an equivalence theorem of the minimax form for this design problem, show that the optimum criterion value [phi][alpha]*=[phi]([xi][alpha]*) is continuous in [alpha] and give a condition for [phi][alpha]* being differentiable with respect to [alpha].

Suggested Citation

  • Pronzato, Luc, 2004. "A minimax equivalence theorem for optimum bounded design measures," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 325-331, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:325-331
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    Cited by:

    1. Torsten Reuter & Rainer Schwabe, 2023. "Optimal subsampling design for polynomial regression in one covariate," Statistical Papers, Springer, vol. 64(4), pages 1095-1117, August.

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