Optimal designs for approximating the path of a stochastic process |
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Institution: | 1. Department of Mathematics, University Jaume I, E-12071, Castellón, Spain;2. Department of Mathematics and Mathematical Statistics, Umeå University, Umeå, Sweden |
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Abstract: | We consider a centered stochastic process {X(t):t ∈ T} with known and continuous covariance function. On the basis of observations X(t1), …, X(tn) we approximate the whole path by orthogonal projection and measure the performance of the chosen design d = (t1, …, tn)′ by the corresponding mean squared L2-distance. For covariance functions on T2 = 0, 1]2, which satisfy a generalized Sacks-Ylvisaker regularity condition of order zero, we construct asymptotically optimal sequences of designs. Moreover, we characterize the achievement of a lower error bound, given by Micchelli and Wahba (1981), and study the question of whether this bound can be attained. |
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