Wynn, H. P. (1972). Results in the theory and construction of D-optimum experimental designs. J. Roy. Statist. Soc. Ser. B, 34:133--147. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Variational Calculus in Space of Measures and Optimal Design - Molchanov, Zuyev (2000) (1 citation) (Correct)
....within the design framework for an arbitrary . To circumvent this difficulty, it is quite typical in the optimal design literature to replace (1.3) by the following definition of the directional derivative: D ( lim t#0 t 1 ( 1 t) t ) 1. 4) Atkinson and Donev, 1992; Wynn, 1972). Now (1 t) t is a probability measure for t 2 [0; 1] if both and are probability measures. This definition of the directional derivative is used to construct the steepest (with respect to differential operator D) descent algorithms for finding optimal designs when it is not possible ....
....measure for t 2 [0; 1] if both and are probability measures. This definition of the directional derivative is used to construct the steepest (with respect to differential operator D) descent algorithms for finding optimal designs when it is not possible to obtain analytical solutions (Wynn, 1972). However, the descent related to (1.4) is only asymptotically equivalent to the true steepest descent as defined by D in (1.3) Indeed, it is easy to see from the definitions that D ( D ( Thus, the descent direction determined by minimising D ( over all ....
Wynn, H. P. (1972). Results in the theory and construction of D-optimum experimental designs. J. Roy. Statist. Soc. Ser. B, 34:133--147.
Variational Analysis of Functionals of a Poisson Process - Molchanov, Zuyev (1997) (2 citations) (Correct)
.... in this problem is given by Delta(x; Pi) det M ( Pi ffi x ) Gamma det M ( Pi) det(M ( Pi) f(x) f(x) Gamma det M ( Pi) Recall that for any k Theta k positive de nite matrix A and a 1 Theta k row b one has det(A b b) det A Gamma 1 = bA Gamma1 b ; see, e.g. [28]. Therefore Delta (x) E det M ( Pi) f(x)M Gamma1 ( Pi)f (x) E det M ( Pi) d(x; Pi) k X i;j=1 ( Gamma1) i j f i (x)f j (x) E det Z f # Thetaae (y) f # Thetaae (y) Pi(dy) where f # Thetaae (y) is the row of f m (y) m 2 f1; kg n fi; jg. In particular, ....
Wynn, H.-P. (1972) Results in the theory and construction of D-optimum experimental designs. J. Roy. Statist. Soc. Ser. B 34, 133147.
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