D-optimal designs for Poisson regression with synergetic interaction effect

• Fritjof Freise ^[2] ; Ulrike Graßhoff ^[3] ; Frank Röttger ^[1] ; Rainer Schwabe ^[4]
  1. [1] Université de Genève

     Université de Genève

     Genève, Suiza

     
  2. [2] Department of Biometry, Epidemiology and Information Processing, University of Veterinary Medicine Hannover, Bünteweg 2, 30559, Hannover, Germany
  3. [3] School of Business and Economics, Humboldt-University Berlin, Unter den Linden 6, 10099, Berlin, Germany
  4. [4] nstitute for Mathematical Stochastics, Otto-von-Guericke-University Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 30, Nº. 4, 2021, págs. 1004-1025
• Idioma: inglés
• DOI: 10.1007/s11749-020-00752-w
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• Resumen

  • We characterize D-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of constant intensity. This approach leads to a substantial reduction in complexity as properties of the sensitivity can be treated along and across the contours separately. Furthermore, some extensions of this result to higher dimensions are presented.