Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 2

DE- and EDPM- compound optimality for the information and probability-based criteria

Sayfa
580–591
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, two numerical examples are given to illustrate the potentiality of the proposed compound criteria.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Several optimality criteria have been considered in the literature as information-based criteria.
📊
Temel Bulgular & Veri:The probability- based criteria have been recently proposed for maximizing the probability of a desired outcome.
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Sonuç & Katkı:Finally, two numerical examples are given to illustrate the potentiality of the proposed compound criteria.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

Several optimality criteria have been considered in the literature as information-based criteria. The probability- based criteria have been recently proposed for maximizing the probability of a desired outcome. However, designs that are optimal for the information- based criteria may be inadequate for probability- based criteria. This paper introduces the DE- and EDPM – optimum designs for multi aims of optimalityforGeneralizedLinearModels(GLMs). Anequivalencetheorem is proved for both compound criteria. Finally, two numerical examples are given to illustrate the potentiality of the proposed compound criteria.

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Bu Makaleye Atıf Yap

Hassanein, W. A., Kilany, N. M. (2022). DE- and EDPM- compound optimality for the information and probability-based criteria. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 580–591. https://ajindex.com/articles/529743

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Kaynakça (17)

  1. Agresti, A., “Foundations of Linear and Generalized Linear Models”. John Wiley & Sons, Inc., Hoboken, New Jersey, 2015
  2. Atkinson, A., “DT-Optimum Designs for Model Discrimination and Parameter Estima- tion”. Journal of Statistical Planning and Inference, 138, 56-64, 2008
  3. Atkinson, A., Donev, A. and Tobias, R., “Optimum Experimental Designs, with SAS”. Oxford university press, New York, 2007
  4. Boyd, S. and Vandenberghe, L., “Convex Optimization”. Cambridge University Press, Cam- bridge, 2004
  5. Chang, F. and Heiligers, B., “E-Optimal Designs for Polynomial Regression without Inter- cept”. Journal of Statistical Planning and Inference, 55, 371-387, 1996
  6. Clyde, M. and Chaloner, K., “The Equivalence of Constrained and Weighted Designs in Multiple Objective Design Problems”. Journal of the American Statistical Association, 91, 1236-1244, 1996
  7. Corana, A., Marchesi, M., Martini, C. and Ridella, S., “Minimizing Multimodal Functions of Continuous Variables with the ‘Simulated Annealing’ Algorithm”. ACM Trans. Math. Software, 13, 262–280, 1987
  8. Denman, N. G., McGree, J. M., Eccleston, J. A. and Duffull, S. B., “Design of Experiments for Bivariate Binary Responses Modelled by Copula Functions”. Computational Statistics & Data Analysis, 55, 1509-1520, 2011
  9. Dette, H., “A Note on E-Optimal Designs for Weighted Polynomial Regression”. Annals of Statistics, 21, 767-771, 1993
  10. Dette, H. and Studden, W., “Geometry of E-Optimality”. Annals of Statistics, 21, 416-433, 1993
  11. Dette, H. and Haines, L., “E-optimal Designs for Linear and Nonlinear Models with two Parameters”. Biometrika, 81, 739–754, 1994
  12. Dette, H., Melas,V. and Pepelyshev, A., “Local c-optimal and E-optimal Designs for Expo- nential Regression Models”. AISM, 58: 407–426, 2006
  13. Dette, H. and Wong, W.K., “E-optimal designs for the Michaelis Menten Model”. Statistics &Probability Letters, 44, 405–408, 1999
  14. Ehrenfeld, E., “On the Efficiency of Experimental Design”. Annals of Mathematical Statis- tics, 26, 247–255, 1955
  15. Heiligers, B., "Computing E–Optimal Polynomial Regression Designs”. Journal of Statistical Planning and Inference, 55, 219–233, 1996
  16. Heiligers, B., "E–Optimal Designs for Polynomial Spline Regression”. Journal of Statistical Planning and Inference, 75, 159-172, 1998
  17. Kilany, N. M., “Optimal Designs for Probability-based Optimality, Parameter Estimation and Model Discrimination”. Journal of the Egyptian Mathematical Society