1915

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

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.

PDF

___

[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, 25, 212- 215, 2017.
[18] Kilany, N. M. and Hassanein, W. A., “AP- Optimum Designs for Minimizing the Average Variance and Probability-Based Optimality”. REVSTAT – Statistical Journal, In Press, 2017.
[19] Mcgree, J. M. and Eccleston, J. A., “Probability-Based Optimal Design”. Australian and New Zealand Journal of Statistics, 50 (1), 13- 28, 2008.
[20] McGree, J. M., Duffull, S. B. and Eccleston, J. A., “Compound Optimal Design Criteria for Nonlinear Models”. Journal of Biopharmaceutical Statistics, 18, 646-661, 2008.
[21] Mwan, D. M., Kosgei, M. K. and Rambaei, S. K., “DT- optimality Criteria for Second Order Rotatable Designs Constructed Using Balanced Incomplete Block Design”. British Journal of Mathematics & Computer Science, 22(6), 1-7, 2017.
[22] Pukelsheim, F. and Studden, W., “E-Optimal Designs for Polynomial Regression”. Annals of Statistics, 21, 402-415, 1993.
[23] Wald, A., “On the Efficient Design of Statistical Investigation”. Annals of Mathematical Statistics, 14, 134–140, 1943.