Strict monotonicity and convergence rate of Titterington's algorithm for computing D-optimal designs

We study a class of multiplicative algorithms introduced by Silvey et al. (1978) for computing D-optimal designs. Strict monotonicity is established for a variant considered by Titterington (1978). A formula for the rate of convergence is also derived. This is used to explain why modifications considered by Titterington (1978) and Dette et al. (2008) usually converge faster.

[1]  Luc Pronzato,et al.  Improvements on removing nonoptimal support points in D-optimum design algorithms , 2007, 0706.4394.

[2]  Xiao-Li Meng,et al.  On the rate of convergence of the ECM algorithm , 1994 .

[3]  S. Silvey,et al.  An algorithm for optimal designs on a design space , 1978 .

[4]  Drew Seils,et al.  Optimal design , 2007 .

[5]  Yaming Yu.  Monotonic convergence of a general algorithm for computing optimal designs , 2009, 0905.2646.

[6]  Luc Pronzato,et al.  Dynamical Search - Applications of Dynamical Systems in Search and Optimization: Interdisciplinary Statistics , 1999 .

[7]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[8]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[9]  D. Titterington.  Estimation of Correlation Coefficients by Ellipsoidal Trimming , 1978 .

[10]  Holger Dette,et al.  Improving updating rules in multiplicative algorithms for computing D-optimal designs , 2008, Comput. Stat. Data Anal..

[11]  Yaming Yu,et al.  Squeezing the Arimoto–Blahut Algorithm for Faster Convergence , 2009, IEEE Transactions on Information Theory.

[12]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[13]  Andrej Pázman,et al.  Foundations of Optimum Experimental Design , 1986 .

[14]  S. Mandal,et al.  Two classes of multiplicative algorithms for constructing optimizing distributions , 2006, Comput. Stat. Data Anal..

[15]  J. Kiefer,et al.  The Equivalence of Two Extremum Problems , 1960, Canadian Journal of Mathematics.