Optimal design of experiments via linear programming - Burclova, Katarina; Pazman, Andrej (Statistical papers (Berlin, Germany), 2016)
We investigate the possibility of extending some results of Pázman and Pronzato (Ann Stat 42(4):1426–1451, 2014 ) to a larger set of optimality criteria. Namely, the problems of computing D -, A -, and E k -optimal designs in a linear regression model are reformulated here as “infinite-dimensional” linear programming problems. The same approach is applied to combination of these optimality criteria and to the “criterion robust” problem of Harman (Metrika 60:137–153, 2004 ). Approximate optimum designs can then be computed by a relaxation method (Shimizu and Aiyoshi in IEEE Trans Autom Control 25(1):62–66, 1980 ), and this is illustrated on various examples.