A stochastic characterization of Loewner optimality design criterion in linear models

Shape optimal design criterion in linear models

“…Sherman 1955), concentration (cf. Eaton and Perlman 1991) and, as it was shown in Liski and Zaigraev (2001), with Loewner optimality (cf. Pukelsheim 1993, Section 4).…”

“…y, that is: In Section 3 we generalize this result. Another motivation for considering stochastic optimality criteria can be found in Liski and Zaigraev (2001). It turns out that the distance stochastic criterion is closely connected with such notions as stochastic ordering (cf.…”

“…Pukelsheim 1993, Section 4). Liski and Zaigraev (2001) also suggested a natural generalization of the DS-criterion. It was called the stochastic convex (SC) criterion.…”

“…Another example of the SC Acriterion is that when A is a class of all subsets from R k which are convex and symmetric with respect to the axes. Due to Lemma 2 from Liski and Zaigraev (2001), the SC A -optimal design for the LSE of b in (2) on the interval ½À1; 1 is of the form fÀ1; 1; 0:5; 0:5g, although there is no SC-optimal design here. Liski and Zaigraev (2001) also proved isotonicity of the SC-criterion relative to Loewner ordering.…”

“…As it follows from Liski and Zaigraev (2001), the SS r -criterion is isotonic relative to Loewner ordering if and only if A r is convex and symmetric with respect to the origin.…”