Optimum designs when the observations are second-order processes |
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Authors: | Carl Spruill WJ Studden |
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Institution: | Georgia Institute of Technology, Atlanta, Georgia 30332 USA;Purdue University, Lafayette, Indiana 47907 USA |
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Abstract: | Let the process {Y(x,t) : t?T} be observable for each x in some compact set X. Assume that Y(x, t) = θ0f0(x)(t) + … + θkfk(x)(t) + N(t) where fi are continuous functions from X into the reproducing kernel Hilbert space H of the mean zero random process N. The optimum designs are characterized by an Elfving's theorem with the closed convex hull of the set {(φ, f(x))H : 6φ 6H ≤ 1, x?X}, where (·, ·)H is the inner product on H. It is shown that if X is convex and fi are linear the design points may be chosen from the extreme points of X. In some problems each linear functional c′θ can be optimally estimated by a design on one point x(c). These problems are completely characterized. An example is worked and some partial results on minimax designs are obtained. |
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Keywords: | 62K05 62710 62M10 62J05 Optimum design estimating a linear form stochastic process reproducing kernel Hilbert space extreme points Elfving's theorem |
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